Rassmotren protsess vozbuzhdeniya sil'nogo kvazistaticheskogo magnitnogo polya pri vzaimodeistvii tsirkulyarno polyarizovannoi volny vysokoi intensivnosti (10^23 Vt/sm^2 i vyshe) s plazmennym sloem. Pokazano, chto v besstolknovitel'nom rezhime vzaimodeistviya prodol'noe magnitnoe pole voznikaet za schet sily radiatsionnogo treniya. Eta spetsificheskaya realizatsiya obratnogo effekta Faradeya mozhet byt' ispol'zovana dlya poiska makroskopicheskikh proyavlenii radiatsionnogo treniya v eksperimentakh, provedenie kotorykh planiruetsya na sverkhmoshchnykh lazernykh ustanovkakh.

Frustratsiya v magnitnykh sistemakh - eto situatsiya, kogda ne vse magnitnye vzaimodeistviya mogut byt' minimizirovany klassicheski odnovremenno, i iz-za etogo razlichnye sostoyaniya mogut byt' polnost'yu vyrozhdeny. Takoe vyrozhdenie usilivaet kvantovye popravki i magnon-magnonnoe vzaimodeistvie, kotorye mogut polnost'yu razrushit' uporyadochennoe sostoyanie. Frustratsiya v dannykh sistemakh mozhet byt' vyzvana kak geometriei reshetki, tak i anizotropnymi vzaimodeistviyami. My pokazhem svoistva takikh sistem detal'no na primere predlozhennoi Alekseem Kitaevym modeli anizotropnykh vzaimodeistvii na geksagonal'noi reshetke, kotoraya otkryla put' k tochno reshaemym spinovozhidostnym fazam.

Weyl semimetal is a solid material with isolated touching points between conduction and valence bands in its Brillouin zone---Weyl points. Low energy excitations near these points exhibit a linear dispersion and act as relativistic massless particles. Weyl points are stable topological objects robust with respect to most perturbations. We study effects of weak disorder on the spectral and transport properties of Weyl semimetals in the limit of low energies. We use a model of Gaussian white-noise potential and apply dimensional regularization scheme near three dimensions to treat divergent terms in the perturbation theory. In the framework of self-consistent Born approximation, we find closed expressions for the average density of states and conductivity. Both quantities are analytic functions in the limit of zero energy. We also include interference terms beyond the self-consistent Born approximation up to the third order in disorder strength. These interference corrections are stronger than the mean-field result and non-analytic as functions of energy. Our main result is the dependence of conductivity on the electron concentration $\sigma = \sigma_0 + A n^{1/3} + (B/\sigma_0) n^{2/3} \ln|n|$ with $A \approx -0.142$ and $B \approx 0.019$.

Generation and detection of spinfull Cooper pairs in conventional superconductors has been intensely pursued by designing increasingly complex magnet-superconductor hybrids. We demonstrate theoretically that magnons with nonzero wavenumbers universally induce a cloud of spinfull triplet Cooper pairs around them in an adjacent conventional superconductor. The resulting composite quasiparticle, termed magnon-cooparon, consists of a spin flip in the magnet screened by a cloud of the spinfull superfluid condensate. Thus, it inherits a large effective mass, which can be measured experimentally. Furthermore, we demonstrate that two magnetic wires deposited on a superconductor serve as a controllable magnonic directional coupler mediated by the nonlocal and composite nature of magnon-cooparons. Our analysis predicts a quasiparticle that enables generation, control, and use of spinfull triplet Cooper pairs in the simplest magnet-superconductor heterostructures.

Vikhri, kotorye poyavlyayutsya v potokakh elektronov, vyzyvayut interes, tak kak yavlyayutsya neoproverzhimym effektom elektronnoi gidrodinamiki. Odnako do sikh po otsutstvovala obshchaya skhema, pozvolyayushchaya svyazat' zavikhrennost', nablyudaemuyu na makrourovne, s mikroskopicheskimi mekhanizmami vzaimodeistviya i rasseyaniya. V nashei rabote my pokazyvaem, chto zavikhrennost' ustoichivym obrazom voznikaet iz-za nelokal'nosti provodimosti \sigma(k), i eto delaet zavikhrennost' svoistvom, kotoroe prisutstvuet v razlichnymi rezhimakh dvizheniya. Pri etom ballisticheskii i gidrodinamicheskii techeniya v realistichnoi geometrii dayut zavikhrennosti, blizkie po absolyutnomu znacheniyu v obeikh rezhimakh. Tem ne menee, ballisticheskie vikhri na neskol'ko poryadkov bolee ustoichivy k prisutstvii protsessov, relaksiruyushchikh impul's, chem gidrodinamicheskie vikhri. Poetomu to, kak legko vikhri gasyatsya besporyadkom i rasseyaniem fononov, mozhet sluzhit' diagnostikoi mikroskopicheskogo proiskhozhdeniya zavikhrennosti v potokakh elektronov.

Poyavivshiisya v poslednyuyu dekadu novyi tip geterostruktur na osnove ZnO/MgZnO pozvolyaet zaglyanut' v fiziku dvumernykh elektronnykh sistem (DES) sushchestvenno dal'she, chem eto bylo vozmozhno v traditsionnykh poluprovodnikakh – kremnii i arsenide galliya. Prichinoi tomu yavlyayutsya sil'nye mezhchastichnye korrelyatsii v sochetanii s malym neodnorodnym ushireniem energeticheskikh urovnei. V etikh dvumernykh sistemakh sravnitel'no legko dostigaetsya parametr Vignera-Zeitsa r_s~5–12. Pri takom nevedomom ranee sochetanii parametrov «ne rabotayut» prezhnie teoreticheskie modeli, desyatiletiyami obkatannye na dvumernom elektronnom gaze. Kachestvennuyu transformatsiyu preterpevayut dazhe «khorosho izuchennye» odnochastichnye yavleniya, takie kak tselochislennyi kvantovyi effekt Kholla (KEKh) – potomu kak vsledstvie kulonovskogo vzaimodeistviya apriori zaputannoi stanovitsya sama sistema urovnei Landau. V prezhnikh magnitotransportnykh issledovaniyakh pokazano, chto samo yavlenie KEKh v geterostrukturakh ZnO ostaetsya, odnako osnovnoe sostoyanie sistemy sil'no modifitsirovano.

V dannoi rabote obnaruzhen ferromagnitnyi perekhod v rezhime tselochislennogo KEKh s chetnymi faktorami zapolneniya v sistemakh na osnove ZnO. Metodami fotolyuminestsentsii i neuprugogo rasseyaniya sveta udalos' okharakterizovat' fazovyi sostav DES, nablyudat' diapazony parametrov sistemy, otvechayushchie ferro- i paramagnitnomu uporyadocheniyu [1]. Postroena fazovaya diagramma dlya sostoyaniya KEKh \nu=2 pri izmenenii parametrov elektronnoi kontsentratsii i ugla naklona magnitnogo polya. Iz fazovoi diagrammy izvlecheny perenormirovannye fermi-zhidkostnye parametry dlya effektivnoi massy i spinovoi vospriimchivosti DES. Pokazano, chto imenno vozrastayushchaya rol' kulonovskikh korrelyatsii pri umen'shenii kontsentratsii DES yavlyaetsya pervoprichinoi dannogo fazovogo prevrashcheniya.

Pomimo fenomenologii ferromagnitnogo perekhoda v nastoyashchei rabote proveden analiz mikroskopicheskogo mekhanizma etogo yavleniya. Metodom neuprugogo rasseyaniya sveta proslezheno povedenie nizkoenergeticheskikh kollektivnykh vozbuzhdenii pri izmenenii kontsentratsii DES i pokazano, chto ferromagnitnyi perekhod nastupaet vsledstvie smyagcheniya tsiklotronnogo spin-flip vozbuzhdeniya (CSFE), i posleduyushchego lavinoobraznogo perekhoda elektronov mezhdu sosednimi urovnyami Landau s protivopolozhnymi spinovymi proektsiyami [2]. Analogichno, v terminakh kollektivnykh spinovykh vozbuzhdenii ob'yasnyaetsya i obratnyi perekhod ferromagnetik-paramagnetik [3]. V oboikh sluchayakh pokazana klyuchevaya rol' nalichiya magnitorotonnogo minimuma v dispersii spinovykh vozbuzhdenii.

Eksperimental'nye dannye po energii vovlechennykh kollektivnykh vozbuzhdenii khorosho soglasuyutsya s raschetom, provedennym metodami tochnoi diagonalizatsii i ekranirovannogo priblizheniya Khartri-Foka [2,3].

[1] A.B.Vankov, B.D.Kaysin, I.V.Kukushkin, Phys.Rev.B 96, 235401 (2017).
[2] A.B.Vankov, B.D.Kaysin, I.V.Kukushkin, Phys.Rev.B 98 121412(R) (2018).
[3] A.B.Vankov, I.V.Kukushkin, Phys.Rev.B 104, 165144 (2021).

V ochen' chistykh obraztsakh normal'nykh provodnikov elektrony provodimosti pri nizkikh temperaturakh mogut formirovat' vyazkuyu elektronnuyu zhidkost'. V rabote izuchayutsya vysokochastotnye techeniya takoi zhidkosti v magnitnom pole. Pokazano, chto ee koeffitsienty sdvigovoi vyazkosti imeyut rezonans pri chastote techeniya, blizkoi k udvoennoi tsiklotronnoi chastote elektronov. Takoi rezonans obuslovlen sobstvennoi dinamikoi tenzora vyazkikh napryazhenii elektricheski zaryazhennoi zhidkosti v magnitnom pole i, pri otsutstvii rezonansov na drugikh garmonikakh tsiklotronnoi chastoty, yavlyaetsya priznakom realizatsii gidrodinamicheskogo vysokochastotnogo transporta. Pokazano, chto v ochen' chistykh i dostatochno shirokikh obraztsakh predskazannyi vyazkouprugii rezonans proyavlyaetsya v koeffitsiente zatukhaniya magnitoplazmonov. Izucheny takzhe poperechnye sdvigovye magnitozvukovye volny, kotorye mogut vozbuzhdat'sya v elektronnoi zhidkosti pri dostatochno bol'shoi sile mezhchastichnogo vzaimodeistviya. V ramkakh gidrodinamicheskogo priblizheniya rasschitan ikh zakon dispersii i ikh vklad v lineinyi otklik zhidkosti na radiochastotnoe elektricheskoe pole. Chastota poperechnykh voln v predele malykh volnovykh vektorov ravna udvoennoi tsiklotronnoi chastote. Eto privodit, dlya techenii v dostatochno uzkikh obraztsakh, k proyavleniyu vyazkouprugogo rezonansa za schet komponenty techeniya, sformirovannoi magnitozvukovymi volnami. Dlya mikroskopicheskogo obosnovaniya ispol'zovannogo gidrodinamicheskogo opisaniya bylo pokazano, chto kineticheskoe uravnenie dlya vysokochastotnoi dinamiki kvazichastits elektronnoi fermi-zhidkosti v predele bol'shoi velichiny mezhchastichnogo vzaimodeistviya svoditsya k gidrodinamicheskim uravneniyam Nav'e-Stoksa s perenormirovannymi koeffitsientami. Tsiklotronnaya chastota, vkhodyashchaya v vysokochastotnuyu vyazkost' v etikh uravneniyakh, perenormiruetsya mezhchastichnym vzaimodeistviem i stanovitsya otlichnoi ot neperenormiruemoi "obychnoi" tsiklotronnoi chastoty, opredelyayushchei tsiklotronnyi rezonans. Dany argumenty v pol'zu togo, chto vozbuzhdenie izuchennykh poperechnykh magnitozvukovykh voln ob'yasnyaet anomal'nyi pik v fotosoprotivlenii naibolee kachestvennykh vysokopodvizhnykh kvantovykh yam GaAs, v kotorykh, po-vidimomu, realizuetsya gidrodinamicheskii rezhim elektronnogo transporta.

An open quantum system is continuously "monitored" by its environment, so its dynamics consists of two competing processes: unitary evolution, which generates entanglement and generically leads to chaotic dynamics, and non-unitary operations resulting from measurements and noisy couplings to the environment, that tend to irreversibly destroy quantum information by revealing it. A minimal model that captures these competing processes consists of a quantum circuit made up of random unitary gates interlaced with local projective measurements. Remarkably, this minimal model undergoes a dynamical phase transition as the rate of measurements is increased. In this talk, I will introduce an exact replica statistical mechanics approach to this problem, and show that the transition is described by a CFT with central charge c=0. I will also present numerical results on the spectrum of this theory using a transfer matrix approach that indicate multifractal scaling of correlation functions at the critical point, reflected in a continuous spectrum of scaling dimensions.

Dvumernye elektronnye sistemy v kvantuyushchem magnitnom pole predstavlyayut isklyuchitel'nyi interes s tochki zreniya vovlecheniya kvazichastits s ne bozevskoi i ne fermievskoi statistikoi (enionnoi), v oblast' prikladnykh fizicheskikh zadach. Drobnye sostoyaniya DKEKh yavlyayutsya edinstvennymi na segodnyashnii den' eksperimental'no realizovannymi kandidatami na rol' sistemy kvazichastits s enionnoi statistikoi. Dlya vyyavleniya statisticheskikh i termodinamicheskikh svoistv enionnykh sistem eksperimental'no sformirovan makroskopicheskii ansambl' neitral'nykh vozbuzhdenii v DKEKh 1/3. Okazalos', chto vozbuzhdeniya imeyut sverkhdlinnye vremena zhizni i proyavlyayut bozevskie svoistva.

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Odnim iz glavnykh kandidatov na rol' vzaimodeistviya, privodyashchego k sverkhprovodimosti v pniktidakh i khal'kogenidakh zheleza vystupayut spinovye fluktuatsii. Oni privodyat k vozniknoveniyu sverkhprovodyashchego parametra poryadka s±-tipa. Dannoe neobychnoe sverkhprovodyashchee sostoyanie obladaet odnim zamechatel'nym svoistvom: ono mozhet pereiti v s++-sostoyanie pri uvelichenii nemagnitnogo besporyadka. Obnaruzhenie takogo perekhoda podtverdit sushchestvovanie s±-sostoyaniya v chistykh sverkhprovodnikakh na osnove zheleza i, sootvetstvenno, podtverdit spin-fluktuatsionnyi mekhanizm sverkhprovodimosti. V dannoi rabote issledovana temperaturnaya zavisimost' londonovskoi glubiny proniknoveniya v ramkakh podkhoda Eliashberga dlya dvukhzonnoi modeli s++- i s±-sverkhprovodnikov s nemagnitnymi primesyami i opredelen nabor kharakternykh osobennostei, ukazyvayushchikh na nalichie perekhoda s±→s++, a takzhe provedeno kriticheskoe sravnenie s imeyushchimisya eksperimental'nymi dannymi.

We study an array of strongly correlated quantum dots of complex SYK type and account for the effects of quadratic terms added to the SYK Hamiltonian; both local terms and inter-dot tunneling are considered in the non-Fermi-liquid temperature range T >> T_FL Electric σ(ω, p) and thermal κ(ω, p) conductivities are calculated as functions of frequency and momentum, for arbitrary values of the particle-hole asymmetry parameter. At low frequencies ω << T we find the Lorentz ratio L = κ(0, 0)/σ(0, 0) to be non-universal and temperature-dependent. At ω >> T the conductivity σ(ω, p) contains a pole with nearly linear dispersion ω ≈ sp ln (ω/T) reminiscent of the "zero-sound", known for Fermi-liquids.

We propose a superconducting quantum circuit based on a general symmetry principle—combinatorial gauge symmetry—designed to emulate topologically ordered quantum liquids and serve as a foundation for the construction of topological qubits. The proposed circuit exhibits rich features: in the classical limit of large capacitances its ground state consists of two superimposed loop structures; one is a crystal of small loops containing disordered U(1) degrees of freedom, and the other is a gas of loops of all sizes associated with Z2 topological order. We show that these classical results carry over to the quantum case, where phase fluctuations arise from the presence of finite capacitances, yielding Z2 quantum topological order. A key feature of the exact gauge symmetry is that amplitudes connecting different Z2 loop states arise from paths having zero classical energy cost. As a result, these amplitudes are controlled by dimensional confinement rather than tunneling through energy barriers. We argue that this effect may lead to larger energy gaps than previous proposals that are limited by such barriers, potentially making it more likely for a topological phase to be experimentally observable. Finally, we discuss how our superconducting circuit realization of combinatorial gauge symmetry can be implemented in practice.

PRX QUANTUM 2, 030341 (2021)

(Neobychnoe vremya: 16.00! Translyatsiya: Zoom)

Majorana zero modes are a much sought-after consequence of one-dimensional topological superconductivity. Here we show that, in turn, zero modes accompanying dynamical instanton events strongly enhance - in some cases even enable - superconductivity. We find that the dynamics of a one-dimensional topological triplet superconductor is governed by a theta-term in the action. For isotropic triplets, this term enables algebraic charge-2e superconductivity, which is destroyed by fluctuations in non-topological superconductors. For anisotropic triplets, zero modes suppress quantum phase slips and stabilize superconductivity over a large region of the phase diagram. We present predictions of correlation functions and thermodynamics for states of topologically enhanced superconductivity.

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Vychislen srednii dzhozefsonovskii tok I_c*\sin\phi cherez izolyator Andersona bol'shoi tolshchiny (mnogo bol'she dliny lokalizatsii \xi). Pokazano, chto amplituda toka ubyvaet priblizitel'no eksponentsial'no s tolshchinoi bar'era, odnako effektivnaya dlina ubyvaniya vo mnogo raz prevyshaet dlinu lokalizatsii elektronnykh sostoyanii v izolyatore. Tem samym, ob'yasnen davno izvestnyi eksperimental'nyi rezul'tat, izvestnyi pod nazvaniem "long range Josephson effect". Razvitaya teoriya pokazyvaet chto kachestvenno etot effekt svyazan s a) sil'nymi fluktuatsiyami volnovykh funktsii lokalizovannykh sostoyanii, i b) mottovskimi rezonansami na parakh lokalizovannykh sostoyanii. Pokazano, chto pri tolshchine izolyatora L bol'she "mottovskoi dliny" L_M = \xi \ln(\delta_\xi/\Delta) izmenyaetsya znak amplitudy toka I_c, to est' realizuetsya sverkhprovodyashchii "pi-kontakt".

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In the first part, I will briefly summarize our current understanding of the relation between Anderson localization on random regular graphs and many-body localization (MBL) [1]. In the second part, I will review several recent preprints, which question observability of genuine MBL transition in state-of-the-art numerical simulations [2,3,4].

[1] Tikhonov, Mirlin; Annals of Physics, 168525
[2] Morningstar, Colmenarez, Khemani, Luitz, Huse; arXiv:2107.05642
[3] Sels; arXiv:2108.10796
[4] Sierant, Zakrzewski; arXiv:2109.13608

(Ceminar v normal'nom rezhime, s translyatsiei: Zoom)

V samoe poslednee vremya nablyudaetsya interes k nelokal'nomu kvazichastichnomu otkliku v strukturakh s maioranovskimi nanoprovolokami [1]. Predpolagaetsya, chto issledovanie nelokal'noi provodimosti pomozhet prolit' svet na proiskhozhdenie podshchelevogo transporta i nadezhno ustanovit' tochku topologicheskogo fazovogo perekhoda. Ya rasskazhu ob eksperimente [2], postavlennom v trivial'noi faze i demonstriruyushchem vtorichnost' nelokal'noi provodimosti po sravneniyu s nelokal'nym teplovym otklikom. V osnove eksperimenta lezhit sochetanie nelokal'nogo transporta s nelokal'nym shumovym otklikom, pozvolivshee prodemonstrirovat' effektivnoe razdelenie tepla i zaryada na sverkhprovodyashchem kontakte. V rezul'tate takogo razdeleniya srednii zaryad proshedshei kvazichastitsy okazyvaetsya blizok k nulyu, tak chto nelokal'nyi kvazichastichnyi transport yavlyaetsya zaryadovo-neitral'nym. Krome togo, nablyudenie predskazannogo nedavno Andreevskogo vypryamleniya [3] demonstriruet, chto etot effekt ne yavlyaetsya unikal'nym svoistvom topolicheskogo fazovogo perekhoda.

[1] D. Puglia et al., Phys. Rev. B 103, 235201 (2021) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.103.235201

[2] A.O. Denisov et al., Semicond. Sci. Tech., 36, 09LT04 (2021) https://iopscience.iop.org/article/10.1088/1361-6641/ac187b/meta

[3] T.Ö. Rosdahl et al., Phys. Rev. B 97, 045421 (2018) https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.045421

A mechanism of electron-mediated pumping of heat in the absence of net charge transfer is proposed. It may be realized in charge-neutral electron systems, such as graphene, coupled to an external electric potential. The flow of heat in this pumping cycle is not accompanied by a buildup of voltage along the system, which offers advantages over traditional thermoelectric cooling setups. Efficiency of heat pumping and magnitude of heat flux are studied in the hydrodynamic regime for weak disorder. In a pristine system, even for an infinitesimal pumping potential the heat flux remains finite. In particular, for a potential in the form of a traveling wave moving with velocity c the pumping is perfect; the entire heat content of the electron liquid is advected with velocity c. For a general pumping cycle the heat flux is determined by the cycle geometry and disorder strength.

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We consider a planar SIS-type Josephson junction between diffusive superconductors (S) through an insulating tunnel interface (I). We construct fully self-consistent perturbation theory with respect to the interface conductance. As a result, we find correction to the first Josephson harmonic and calculate the second Josephson harmonic. At arbitrary temperatures, we correct previous results for the nonsinusoidal current-phase relation in Josephson tunnel junctions, which were obtained with the help of conjectured form of solution. Our perturbation theory also describes the difference between the phases of the order parameter and of the anomalous Green functions.

[1] A.S. Osin and Ya.V. Fominov, arXiv:2105.05786

Recently, the standard picture of ALT in long-range systems [1, 2] has been argued from the following perspective. There have been reported [3-6] several counterintuitive examples of single-particle systems with long-range hopping, where almost all states are (at least power-law) localized even in a nominally ergodic regime, where the standard locator expansion breaks down [1, 2]. Some of these "new" models demonstrate critical behavior [3, 4] for disorder strengths below the ones at the ALT [1, 2]. In the other ones [6, 7] wave-function spatial decay rates obey a "mysterious" duality [6] mapping different powers of power-law bending [2]. The seminal paper on second-type models [7] has been unnoticed until recently.
What is the striking difference between the standard long-range models [1-2] and the new ones [3-8]? The systems [3-8] belong to a new universality class where correlations of hopping terms play a significant role in the localization properties. In my talk I address this intriguing question. I present a general approach applicable to all such models and uncover the role of correlations and the origin of the duality [A]. This method is based on the localization-delocalization principles both in the coordinate and in the momentum space. I will show that the so-called Mott's criterion (which is shown to be the sufficient criterion of ergodic delocalization) and the Anderson criterion (which is shown to be the sufficient criterion of localization) are not complimentary. There is a gap between their regions of validity where the non-ergodic extended phases and the novel correlation-induced localization may occur. To illustrate the above mentioned principles I will consider the models either with infinitely-long range hopping [3-5] or with power-law decaying ones [1-2, 6-8, A-F] and focus mostly on the latter class. The well-known example of the latter class is the power-law random banding matrices (PLRBM).
Furthermore, we extend the above mentioned models by a new class that bridge between the models with uncorrelated hopping and those with fully correlated ones. These are the models with translation-invariant (TI) long-range hopping terms which allow one to apply the above mentioned principles both in the coordinate and momentum spaces completing their phase diagrams. A remarkable feature of these random TI models is the presence of the Poisson spectral statistics within the delocalized phase. This goes against the common wisdom that the Poisson statistics signals of localization. The reason for such a behavior is that the Poisson spectral statistics emerges in the parameter region where the states in the coordinate space are, indeed, extended and weakly ergodic but those in the momentum space are localized. The common wisdom assumes by default that the states in momentum space are always chaotically extended. The TI models introduced in this paper constitute a class of models where this assumption fails. If time permits, I will mention some of the recent results on the topic for higher-dimensions, anisotropic models, and the effects of partial correlations in TI models.

Literature:
[1] L. S. Levitov, Europhy. Lett. 9, 83 (1989); Phys. Rev. Lett. 64, 547 (1990).
[2] A. D. Mirlin, Y. V. Fyodorov, F.-M. Dittes, J. Quezada, and T. H. Seligman, Phys. Rev. E 54, 3221 (1996).
[3] H. K. Owusu, K. Wagh, and E. A. Yuzbashyan, J. Phys. A: Math. Theor. 42, 035206 (2009).
[4] A. Ossipov, J. Phys. A 46, 105001 (2013).
[5] G. L. Celardo, R. Kaiser, and F. Borgonovi, Phys. Rev. B 94, 144206 (2016).
[6] X. Deng, V. E. Kravtsov, G. V. Shlyapnikov and L. Santos, Phys. Rev. Lett. 120, 110602 (2018).
[7] A. L. Burin and L. A. Maksimov, JETP Lett. 50, 338 (1989).
[8] J. T. Cantin, T. Xu, and R. V. Krems, Phys. Rev. B 98, 014204 (2018).
[A] P. Nosov, I. M. K., V. E. Kravtsov, “Correlation-induced localization” Phys. Rev. B 99, 104203 (2019) [arXiv:1810.01492]
[B] P. A. Nosov, I. M. K., “Robustness of delocalization to the inclusion of soft constraints in long-range random models”, Phys. Rev. B 99, 224208 (2019) [arXiv:1904.11509].
[C] A. Kutlin, I. M. K., “Renormalization to localization without a small parameter”, SciPost Phys. 8, 049 (2020) [arXiv:2001.06493]
[D] X. Deng, A. L. Burin, I. M. K., “Anisotropy-driven localization transition in quantum dipoles” [arXiv:2002.00013]
[E] A. G. Kutlin, I. M. K., "Multifractality emergence in energy stratified random models", in preparation
[F] W. C. Tang, I. M. K., “Non-ergodic delocalized phase with Poisson level statistics”, in preparation

(Seminar v normal'nom rezhime, s translyatsiei: Zoom)

We consider a non-equilibrium generalization of the mixed SYK4 +SYK2 model and calculate the energy dissipation rate W(ω) that results due to periodic modulation of random quadratic matrix elements with a frequency ω. We find that W(ω) possesses a peak at ω close to the polaron energy spliting E1 found recently in [1], demonstrating physical significance of the energy E1. Next, we study the effect of energy pumping with a finite amplitude A1 at the resonance frequency ω = E1 and calculate, in presence of pumping, non-equilibrium boson distribution function and dissipation rate due to low-frequency parametric modulation. At sufficiently strong pumping, low-frequency dissipation rate recovers its large value, pertinent to the pure SYK4 limit.

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Doklad po rabote arXiv:2101.08535

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V rabote byla teoreticheski issledovana nakachka magnonnykh par v Dirakovskie tochki spektra magnonov ferromagnetika na reshetke tipa pchelinye soty. V chastnosti byl rassmotren tak nazyvaemyi protsess Sula vtorogo roda, v kotorom, blagodarya vzaimodeistviyu mezhdu magnonami, dva kvanta elektromagnitnogo polya nakachki pogloshchayutsya sistemoi, v rezul'tate chego sozdaetsya para magnonov. Byl izuchen bozonnyi analog kuperovskoi lestnitsy protsessov pererasseyaniya takoi pary magnonov, i bylo pokazano, chto pri opredelennykh usloviyakh pary dirakovskikh magnonov yavlyayutsya naibolee neustoichivymi v sisteme, a chastota polya nakachki, sootvetstvuyushchaya energii dirakovskikh tochek, - rezonansnoi. Nami vydvinuto predpolozhenie, chto v rezul'tate takoi neustoichivosti ferromagnetik perekhodit v novoe sostoyanie s nulevoi namagnichennost'yu.

V.A Zyuzin, "Pumped Dirac magnons paired state”, arXiv:2012.12051

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Rassmatrivaetsya zadacha o strukture sostoyanii, lokalizovannykh v kore vikhrya, raspolozhennogo vblizi granitsy mezhdu dvumya chistymi sverkhprovodnikami. Granitsa predpolagaetsya dostatochno prozrachnoi, s koeffitsientom otrazheniya R<<1, chto predstavlyaet soboi predel obratnyi standartnomu priblizheniyu tunnel'nogo gamil'toniana, primenimomu dlya plokho prozrachnykh granits. Pokazano, chto nalichie granitsy privodit k obrazovaniyu shcheli v spektre lokalizovannykh v kore vikhrya nizkoenergeticheskikh sostoyanii , kotoraya imeet poryadok velichiny E_g ~ Δ sqrt(R), chto uzhe pri ochen' malykh koeffitsientakh otrazheniya prevyshaet srednee rasstoyanie w_0 ~ Δ^2/E_F mezhdu urovnyami kiral'noi vetvi spektra. Shchel' maksimal'na, kogda vikhr' raspolozhen pryamo na defekte, umen'shaetsya po mere uvelicheniya rasstoyaniya b do defekta i zakryvaetsya pri k_F b ~ E_g/w_0. Issledovano takzhe obobshchenie zadachi na sluchai razlichnykh konfiguratsii s neskol'kimi granitsami (periodicheskie struktury, peresechenie dvukh lineinykh granits, «zvezda» s neskol'kimi luchami). Vo vsekh sluchayakh shchel' v spektre sokhranyaetsya, odnako v sluchae peresekayushchikhsya granits voznikaet sil'no vyrazhennyi effekt soizmerimosti, kogda velichina shcheli sushchestvenno zavisit ot togo, naskol'ko khorosho ugol peresecheniya (v edinitsakh polnoi okruzhnosti) approksimiruetsya ratsional'noi drob'yu.

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Otlichnaya ot nulya ob'emnaya vyazkost' signaliziruet o narushenii masshtabnoi invariantnosti. My pokazali, chto besporyadok v dvumernom nevzaimodeistvuyushchem elektronnom gaze v perpendikulyarnom magnitnom pole privodit k nenulevoi ob'emnoi vyazkosti. Polucheno analiticheskoe vyrazhenie dlya usrednennoi po besporyadku ob'emnoi vyazkosti v bornovskom priblizhenii. Eta ostatochnaya ob'emnaya vyazkost' daet nizhnyuyu otsenku dlya ob'emnoi vyazkosti v dvumernykh elektronnykh sistemakh.

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Poslednee vremya nablyudaetsya bol'shoi eksperimental'nyi i teoreticheskii interes k geterostukturam, sostoyashchim iz ferromagnetika s magnitnymi skirmionami i sverkhprovodnika vtorogo roda. Obuslovleno eto perspektivoi sozdaniya ustoichivogo ob'ekta iz skirmiona i vikhrya s posleduyushchei vozmozhnost'yu manipulirovat' etoi sistemoi. V nashei rabote [1] izuchaetsya vzaimodeistvie neelevskogo skirmiona i pirlovskogo vikhrya za schet magnitnogo polya razmagnichivaniya. Nam udalos' pokazat', chto pri nekotorykh obstoyatel'stvakh pirlovskii vikhr' stremitsya raspolozhit'sya na nenulevom rasstoyanii ot tsentra skirmiona i chto etot effekt chuvstvitelen k kiral'nosti ferromagnetika. Pri etom kharakternyi razmer skirmiona uvelichivaetsya blagodarya vzaimodeistviyu s vikhrem. Takzhe nasha teoriya predskazyvaet vozmozhnost' spontannogo rozhdeniya pary vikhr'-antivikhr' v prisutstvii skirmiona, chto nakhoditsya v kachestvennom soglasii s rezul'tatami nedavnego eksperimenta [2].

[1] E.S. Andriyakhina. and I.S. Burmistrov “Interaction of a Néel–type skyrmion and a superconducting vortex” // arXiv: https://arxiv.org/abs/2102.05434.
[2] A.P. Petrović et al. “Skyrmion-(Anti)vortex coupling in a chiral magnet-superconductor heterostructure” // Phys.Rev. Lett.126, 117205 (2021).

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With the advent of large arrays of qubits coupled by high fidelity gates the possibility of forming a logical qubit from a large number of faulty physical ones becomes a reality. The problem of finding the probability of logical error, P(L), in a large system of size L ≫ 1 can be mapped into the statistical model, with P(L) that decreases to zero exponentially in the correctable phase. This decrease is sensitive to the probabilities of individual qubit errors, p, measurement errors, q, and error correlations, p_corr. Using a combination of numerical simulations and statistical physics arguments, we identify the regime in the parameter (p , q, p_corr) space in which error correction is possible and we find the logical error dependence on the system size. We argue that for surface code statistical models describing optimal error decoding at the Nishimori line, the critical exponent of the correlation length can be found exactly thereby allowing one to determine P(L) with limited numerical work. As the transition line is approached, we show that the dynamics in the models slows down dramatically due to Griffiths phase physics in these disordered systems, especially at large q. This result as well as the effect of p_corr show that at q ∼ p the error correction is much more difficult than for q ≪ p.

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V etom doklade ya predstavlyu perturbativnoe rassmotrenie, razrabotannoe dlya spetsial'nogo tipa kvantovykh skhem v prisutstvii shuma. Poslednie yavlyayutsya ob'ektom prakticheskogo interesa, poskol'ku oni dopuskayut estestvennuyu realizatsiyu na sushchestvuyushchikh kvantovykh ustroistvakh posredstvom posledovatel'nostei mikrovolnovykh impul'sov v sisteme sverkhprovodyashchikh kubitov. My rassmatrivaem odnomernye periodicheskie (Floke-) diskretnye skhemy, sostavlennye iz tak nazyvaemykh «dual-unitary» dvukhkubitnykh geitov, kotorye mogut byt' grubo opredeleny kak unitarnye kak vo vremennom, tak i v prostranstvennom napravleniyakh. Khotya nekotoroe ponimanie unitarnoi dinamiki v dannom tipe skhem sushchestvuet v literature, ochen' malo izvestno o vliyanii slabykh vozmushchenii, narushayushchikh svoistvo «dual-unitary», ne govorya uzhe pro effekt ot vneshnego shuma v sisteme. My predlagaem prostuyu model' s odnokubitnym shumom i provodim kak chislennyi, tak i analiticheskii analiz modeli, v osnovnom rassmatrivaya povedenie parnogo korrelyatora dvukh operatorov kak funktsii koordinat i vremeni. Poluchennye dannye predostavlyayut nekotoroe kachestvennoe ponimanie opisaniya dannykh neintegriruemykh sistem. Vazhno otmetit', chto razrabotannyi podkhod yavlyaetsya osnovoi dlya bolee detal'nogo izucheniya predlagaemoi modeli v razlichnykh rezhimakh. Nakonets, nashi rezul'taty mogut byt' ispol'zovany kak sposob kharakterizovat' lokal'nyi shum v fizicheskoi sisteme iz mnogikh kubitov.

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Recent demonstration of the first beyond classical quantum computation with a programmable quantum computer [1] opens the path to discovery of new quantum physics phenomena using these hardware systems. Gate model quantum computers used in [1] realize complex multi-qubit evolution in terms of discrete gates, elementary one and two qubit unitary operations, practically realized by a local time-dependent Hamiltonian. In this talk we present a theory and experimental data describing quantum circuit kinetics in such systems, which answers the following question: how does a system initialized in a product state generate highly entangled states and in the case of a non-integrable system approach universal random matrix statistics? We characterize circuit kinetics using time-dependent evolution of out-of-time-order correlators (OTOC) and their ensemble variance. We demonstrate that dynamics of an ensemble average OTOC can be mapped onto a classical population dynamics process, an analog of hydrodynamic description. OTOC variance on the other hand is subject to a “sign problem” and therefore evades efficient classical description. We use ensemble average OTOC to verify hardware output whereas OTOC variance provides a signature of operator entanglement generated in the system [2].

[1] Arute et. al. Nature, Vol 574, 505 (2019)
[2] Mi et. al. arXiv:2101.08870

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We study the propagation of stationary waves in disordered nonlinear media described by the nonlinear Schrödinger equation and show that, for given boundary conditions and a given coherent wave incident on the sample, the number of solutions of the equation increases exponentially with sample size. We also discuss the ballistic case, the sensitivity of the solutions to the change of external parameters, the similarity of this problem to the problem of spin glasses, and time-dependent solutions.

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We consider a noninteracting many-fermion system populating levels of a unitary random matrix ensemble —a generic model of single-particle quantum chaos. We study the corresponding many-particle level statistics by calculating the spectral form factor analytically using algebraic methods of random matrix theory, and match it with an exact numerical simulation. Despite the integrability of the theory, the many-body spectral rigidity is found to have a surprisingly rich landscape. In particular, we find a residual repulsion of distant many-body levels stemming from single-particle chaos, together with islands of level attraction. These results are encoded in an exponential ramp in the spectral form factor, which we show to be a universal feature of nonergodic many-fermion systems embedded in a chaotic medium.

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We developed a theory of electric and thermoelectric conductivity of lightly doped SrTiO3 in the non-degenerate region k_B T ≥ E_F , assuming that the major source of electron scattering is their interaction with soft transverse optical phonons present due to proximity to ferroelectric transition. We have used kinetic equation approach within relation-time approximation and we have determined energy-dependent transport relaxation time τ(E) by the iterative procedure. Using electron effective mass m and electron-transverse phonon coupling constant λ as two fitting parameters, we are able to describe quantitatively a large set of the measured temperature dependences of resistivity R(T) and Seebeck coefficient S(T) for a broad range of electron densities studied experimentally in recent paper by K.Behnia and his colleagues. In addition, we calculated Nernst ratio in the linear approximation over weak magnetic field in the same temperature range.

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Sostoyaniya, opisyvaemye neironnymi setyami, (NQS) privlekayut bol'shoe vnimanie v svyazi s ikh potentsialom stat' ochen' vyrazitel'nym variatsionnym priblizheniem dlya opisaniya kvantovykh mnogochastichnykh sistem. My issleduem faktory, kotorye opredelyayut primenimost' NQS k frustrirovannym magnetikam, obuchaya set' na osnovnykh sostoyaniyakh neskol'kikh Gamil'tonianov s ispol'zovaniem nebol'shogo podmnozhestva znachenii tochno naidennoi volnovoi funktsii. My pokazyvaem, chto sposobnost' seti k obobshcheniyu, -- sposobnost' vosstanovit' osnovnoe sostoyanie po nebol'shomu chislu amplitud i pravil'no predskazat' volnovuyu funktsiyu v ostal'noi chasti Gil'bertova prostranstva, rezko padaet s perekhodom vo frustrirovannyi rezhim. My demonstriruem, chto v nastoyashchii moment, dlya ispol'zovaniya NQS v izuchenii realistichnykh modelei, sushchestvenna imenno obobshchayushchaya sposobnost', a ne vyrazitel'nost' takogo anzatsa. Po rabote: T. Westerhout, N. Astrakhantsev, K. S. Tikhonov, M. I. Katsnelson, A. A. Bagrov, “Generalization properties of neural network approximations to frustrated magnet ground states”, Nature Communications 11, 1593 (2020).

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It is shown that hydrodynamic collision processes in undoped graphene can be described in terms of a Fokker-Planck equation with a fractional derivative, corresponding to Lévy flights in momentum space. Electron-electron collisions give rise to frequent small-angle scattering processes that are interrupted by rare large-angle events. The latter give rise to a superdiffusive phase-space dynamics whose importance for relaxation processes, charge and heat transport, as well as collective modes will be discussed. I will also comment on implications for experiments with surface acoustic waves in graphene-piezoelectric devices.

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V etoi rabote my izuchili nechetnoe po chastote sparivanie, sparivanie Berezinskogo, v neuporyadochennykh provodnikakh. V pervom primere nami byl rassmotren sluchai neuporyadochennoi sistemy vblizi ee perekhoda v izolyator. Tam sovmestnoe deistvie kulonovskogo vzaimodeistviya i rasseyaniya na primesyakh mozhet byt' istochnikom tripletnogo sparivaniya nechetnogo po chastote. V drugom rassmotrennom nami sluchae takoe sparivanie mozhet proiskhodit' vblizi sverkhprovodyashchego perekhoda. V svyazi s etim my rassmotreli sushchestvuyushchie eksperimenty i sdelali predpolozhenie, chto nechetnoe po chastote sparivanie privodit k dielektricheskomu sostoyaniyu. Takoe sostoyanie mozhet byt' rassmotreno kak nezavisimaya faza, sushchestvuyushchaya pered sverkhprovodyashchim perekhodom.

Po rabote Vladimir A. Zyuzin, Alexander M. Finkel’stein, "Odd-frequency spin-triplet instability in disordered electron liquid", arXiv:1912.04258

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We investigate inelastic microwave photon scattering by a transmon qubit embedded in a high-impedance circuit. The transmon undergoes a charge-localization (Schmid) transition upon the impedance reaching the critical value. Due to the unique transmon level structure, the fluorescence spectrum carries a signature of the transition point. At higher circuit impedance, quasi-elastic photon scattering may account for the main part of the inelastic scattering cross-section; we find its dependence on the qubit and circuit parameters. Our theory of total inelastic cross-section explains the measured quality factors of devices consisting of a transmon in a galvanic connection with a high-impedance Josephson junction array.

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Superconducting quantum wires with broken time-reversal and spin-rotation symmetries are emerging as a building block of a topological qubit. By varying the applied external magnetic field or chemical potential such wires may be tuned through the quantum critical point into the topological phase. We investigate signatures of this quantum phase transition in the dynamic response of a Josephson junction. To this end, we compute the finite-frequency admittance Y(ω) of the junction at the topological transition and in its vicinity. At the critical point, the dependence of the admittance on frequency and temperature is universal and determined by the symmetries of the system. We find that, despite the closing of the spectral gap at the transition, the dissipative response may remain weak: ReY(ω) ~ max(ω, T)². This unusual power-law behavior is markedly different from the electromagnetic response of a normal metal. Away from the critical point, a gap opens in the spectrum of the system. The dependence of the admittance on frequency, temperature, and spectral gap has a scaling form. We apply our universal theory to find the scaling functions for different combinations of symmetries.

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Ya rasskazhu o zadachakh, nad kotorymi seichas rabotayu. Rabota nad chast'yu etikh zadach nakhoditsya na stadii podgotovki stat'i k publikatsii, nad nekotorymi – na etape formulirovki voprosa. Primernyi spisok:

1. Neravnovesnyi instanton Korshunova v real'nom vremeni (Ya. Rodionov, A. Dotdaev)
2. Elektronnaya defazirovka na poverkhnosti topologicheskogo izolyatora (I. Gornyi)
3. Eksponentsial'nye khvosty v lokalizatsii so stepennymi pryzhkami (M. Feigel'man, A. Ioselevich)
4. Eilerovskaya neustoichivost' s besporyadkom (S. Evseev, I. Burmistrov, V. Kachorovskii)
5. Korrelyatsii v rasseyannoi na dvukhurovnevoi sisteme volne (N. Masnev, Yu. Makhlin)
6. Sostoyaniya neironnykh setei dlya kvantovykh magnetikov (A. Bagrov, N. Astrakhantsev, T. Westerhout)

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Superconducting films of amorphous Indium Oxide (a:InO) thin films undergo a transition to insulation upon increasing disorder. This quantum phase transition is driven by the localization of preformation of Cooper pairs, which has been evidenced through various unusual spectroscopic properties. The continuous decrease of the critical temperature as the critical disorder approaches indicates a similarly continuous suppression of the superfluid density. In this talk I discuss the fate of the superfluid density in the vicinity of the transition to insulation in a:InO films. To access the superfluid density we conducted a systematic study of the whole plasmon dispersion spectrum of high quality factor microwave resonators made of a:InO, combined with DC resistivity measurements, as a function of disorder. Our main observations are a breakdown of the Mattis-Bardeen theory and a record kinetic inductance of 17nH per square for critical, superconducting samples. Surprisingly, we find that the superfluid density remains finite at the critical disorder. Besides providing new insights to understand the SIT in a:InO, these results may find applications in superconducting quantum circuits where very large inductances are highly desirable.

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Dolinnyi effekt Kholla zaklyuchaetsya v poyavlenii dolinnogo potoka chastits – protivopolozhno napravlennykh potokov v dvukh dolinakh zony Brillyuena. Dolinnyi potok perpendikulyaren iskhodnomu potoku chastits po analogii s tem, kak v spinovom effekte Kholla spinovyi tok poperechen elektricheskomu. Iskhodnyi potok chastits mozhet byt' zadan vneshnim polem, a mozhet byt' obuslovlen uvlecheniem nositelei zaryada ili eksitonov fononami ili fotonami. Tsel' doklada – izlozhit' razvituyu v rabotakh [1,2] teoriyu dolinnogo effekta Kholla v dvumernykh kristallakh v usloviyakh effekta uvlecheniya.

Pokazano, chto imeetsya tri vklada v dolinnyi tok: (i) ot asimmetrichnogo (skew) rasseyaniya (vklyuchaya kogerentnoe rasseyanie na parakh primesyakh i dvukhfononnye protsessy asimmetrichnogo rasseyaniya) i anomal'nye vklady, obuslovlennye (ii) sdvigami volnovykh paketov pri rasseyanii i (iii) ikh anomal'noi skorost'yu. Prodemonstrirovana chastichnaya kompensatsiya anomal'nykh vkladov i ukazana ee fizicheskaya priroda. Vypolneno sopostavlenie dolinnykh tokov elektronov i eksitonov v usloviyakh effekta uvlecheniya s rezul'tatami dlya vneshnego staticheskogo polya i pri nalichii gradienta temperatury chastits (dolinnyi effekt Nernsta) i prodemonstrirovana chuvstvitel'nost' effekta k prirode tyanushchei sily. Dlya eksitonov takzhe provedeno obobshchenie dreifovo-diffuzionnoi modeli, uchityvayushchei dolinnye stepeni svobody, i rasschitany prostranstvennye profili eksitonnoi plotnosti i dolinnoi polyarizatsii.

[1] Valley Hall effect caused by the phonon and photon drag, M. M. Glazov and L. E. Golub, Phys. Rev. B 102, 155302 (1-16) (2020).
[2] Skew Scattering and Side Jump Drive Exciton Valley Hall Effect in Two-Dimensional Crystals, M. M. Glazov and L. E. Golub, Phys. Rev. Lett. 125, 157403 (1-7) (2020).

1. Perevernutyi mayatnik i smezhnye zadachi (N. Stepanov)
2. Kvantovyi transport v maioranovskikh provodakh (D. Antonenko, P. Ostrovskii)
3. Vikhr' u ploskoi stenki (U. Khodaeva)
4. Kogerentnoe proskal'zyvanie fazy (A. Bun'kov, O. Astaf'ev)
5. Fluktuatsii v odnofotonnykh detektorakh (A. Semenov)
6. Neodnorodnyi sverkhtekuchii tok (M. Feigel'man, D. Fazlizhanova)

1. Metallicheskoe povedenie, indutsirovannoe vzaimodeistviem, v dvumernoi neuporyadochennoi ne-Fermi zhidkosti (sovmestno s P. Nosov i S. Raghu)
2. Skirmiony i vikhri v geterostrukturakh sverkhprovodnik-kiral'nyi ferromagnetik (sovmestno s E. Andriyakhina)
3. Magnitnye primesi v neuporyadochennykh sverkhprovodnikakh (sovmestno s A. Lyublinskaya, S. Babkin, B. Pashinskii)
4. Mezoskopicheskie fluktuatsii plotnosti sostoyanii v neuporyadochennykh sverkhprovodnikakh (sovmestno s F. Evers, M. Stosiek)
5. Vyazkost' i svyazannye s nei transportnye koeffitsienty v dvumernom neuporyadochennom elektronom gaze v magnitnom pole (sovmestno s V. Zakharov, M. Goldstein)
6. Fluktuatsii izgiba palochki s uchetom besporyadka (sovmestno s S. Evseev, K. Tikhonov, V. Kachorovskii)

Seminar ochnyi, no s online translyatsiei dlya interesuyushchikhsya, no otsutstvuyushchikh: link na translyatsiyu

Fail s prezentatsiei: zdes'

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
Gaussian Rosenzweig-Porter (GRP) random matrix ensemble is the only one in which the robust multifractal phase have a status of a mathematical theorem. In this paper we suggest an extension of the GRP model, the LN-RP model, by adopting a logarithmically-normal (LN) distribution of off-diagonal matrix elements. We show that large matrix elements from the tail of this distribution give rise to a peculiar weakly-ergodic phase that replaces both the multifractal and the fully-ergodic phases present in GRP ensemble. A new phase is characterized by the broken basis-rotation symmetry which the fully-ergodic phase respects. Thus in addition to the localization and ergodic transitions in LN-RP model there exists also the FWT transition between the two ergodic phases. We formulate the criteria of the localization, ergodic and FWT transitions and obtain the phase diagram of the model. We also suggest a new criteria of stability of the non-ergodic phases and prove that the Anderson transition in LN-RP model is discontinuous, in contrast to its GRP counterpart.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
We study SYK_4 model with weak SYK_2 random terms of typical magnitude Γ beyond the simplest perturbative limit considered previously. In the intermediate range J/N << Γ << J/N^{1/2} of the perturbation strength Γ, fluctuations of the Schwarzian soft mode are suppressed and conformal mean-field solution for the Majorana Green function G(τ) is valid much beyond usual timescale t_∗ ∼ N/J characteristic for pure SYK_4 model. However, high momenta of the probability distribution of the Green function are shown to grow as ln([G(τ)]^p) ∝ p^2 at p >> 1, indicating log-normal shape of the distribution P[G(τ)] . Short-time decay of the out-of-time-order correlation function is characterized by the universal exponent 2πT/\hbar, while the pre-factor is much smaller than in pure SYK_4 model, and shows unusual temperature dependence.

Webinar link: http://bbb2.itp.ac.ru/b/qme-erf-krk
We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temperatures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, κ. This is in striking contrast to the Stokes flow, in which the resistance is independent of κ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magneto-resistance.

https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.106.256804

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Localization of wavefunctions is arguably the most familiar effect of disorder in quantum systems. It has been recently argued [V. Khemani, R. Nandkishore, and S. L. Sondhi, Nature Physics, 11, 560 (2015)] that, contrary to naive expectation, manipulation of a localized-site in the disordered medium may produce a disturbance over a length-scale much larger than the localization-length ξ. Here we report on the observation of this nonlocal phenomenon in electronic transport experiment. Being a wave property, visibility of this effect hinges upon quantum-coherence, and its spatial-scale may be ultimately limited by the phase-coherent length of the disordered insulator. Evidence for quantum coherence in the Anderson-insulating phase may be obtained from magneto-resistance measurements which however are useful mainly in thin-films. The technique used in this work offers an empirical method to measure this fundamental aspect of Anderson-insulators even in relatively thick samples.

In addition, it is recommended by the author to read the following two papers before the seminar:
[1] I. M. Lifshitz, & V. Y. Kirpichenkov, Tunnel transparency of disordered systems, Zh. Eksp. Teor. Fiz. 77, 989 (1979) [Sov. Phys. JETP 50, 499 (1979)].
[2] J. B. Pendry, Quasi-extended electron states in strongly disordered systems, J. Phys. C: Solid State Phys. 20, 733 (1987).

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Recent experiments on twisted bilayer graphene (TBG) near the magic angle have observed spontaneous integer quantum Hall states in the presence of an aligned hexagonal boron nitride (hBN) substrate. These states arise from valley ferromagnetism, and the complete filling of Chern bands. A natural question is whether fractional filling of the same bands would lead to fractional quantum Hall states, i.e. to fractional Chern insulators (FCIs). Using a variant of the continuum model for TBG with zero hopping between AA Moire cites we construct a Laughlin wave function on a real-space torus in full analogy with the Haldane and Rezayi construction for two-dimensional electrons at the lowest Landau-level on a torus.

Webinar: http://bbb2.itp.ac.ru/b/qme-erf-krk
Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-Tc systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, here we introduce a simple model for fermions moving in the deconfined phase of a Z2 gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. By changing the sign of the plaquette term in the toric code, we are able to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which the single particle correlators of the original Fermi operators are gapped, despite the existence of gapless collective modes. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. We are able to access the physics beyond the integrable point using a novel diagrammatic perturbation expansion, which allows us to examine various instabilities of the deconfined phase and to derive the Ising (XY) critical theory at the transition between deconfined and confined metal (semimetal). Finally, the connection to quantum information science allows to discuss an analogue quantum emulator (an array of Majorana Cooper pair boxes) for fermions in Z2 gauge theories. Analytical results for this minimal model pave the way for a better understanding of quantum materials with itinerant fermions and the connection to the toric code opens the potential for simulation using upcoming quantum information techniques.

We develop a theory of quantum T = 0 phase transition (q-SMT) between metal and superconducting ground states in a two-dimensional metal with frozen-in spatial fluctuations δλ(r) of the Cooper attraction constant. When strength of fluctuations δλ(r) exceeds some critical magnitude, usual mean-field-like scenario of the q-SMT breaks down due to spontaneous formation of local droplets of superconducting phase. The density of these droplets grows exponentially with the increase of average attraction constant λ. Interaction between the droplet's order parameters is due to proximity effect via normal metal and scales with distance ∝ 1/rβ, with 2 < β ≤ 3. We account for this interaction by means of a real-space strong-disorder renormalization group (RG). Near the q-SMT the RG flow is, formally, a dual equivalent of the Kosterlitz-Thouless RG. The corresponding line of fixed points describes a Griffiths phase of a metal with large fractal clusters of superconducting islands. Superconducting side is described by a runaway of RG trajectories into the strong-coupling region. Close to the transition point on the SC side, 0 < −δ << 1, RG trajectories possess an extremum as function of the RG parameter ∼ |δ| 1/2 ln(1/T). It results in a very wide temperature range where physical properties are nearly T-independent. This observation may be relevant to the understanding of a ”strange metal” state frequently observed near q-SMT.

Rassmatrivaetsya teoreticheskaya zadacha o rasprostranenii pary fotonov v odnomernom volnovode, v kotoryi pomeshchen periodicheskii massiv dvukhurovnevykh atomov. Otlichiem ot klassicheskoi modeli Dikke yavlyaetsya uchet konechnogo nenulevogo rasstoyaniya mezhdu atomami. Blagodarya fotonnoi blokade - nevozmozhnosti pogloshcheniya dvukh fotonov odnim atomom - mezhdu fotonami voznikaet effektivnoe ottalkivanie. Budet pokazano, chto eto ottalkivanie privodit k obrazovaniyu dvukhfotonnykh sostoyanii, kogda odin iz fotonov lokalizovan, a vtoroi obrazuet stoyachuyu volnu. Takie dvukhchastichnye mody mozhno rassmatrivat' kak analog indutsirovannykh vzaimodeistviem opticheskikh reshetok.

Iz-za apparatnykh ogranichenii sushchestvuyushchie kvantovye protsessory sposobny proizvodit' lish' opredelennyi nabor unitarnykh operatsii nad odnim ili dvumya kvantovymi bitami v techenie konechnogo promezhutka vremeni, posle kotorogo ustroistvo teryaet kogerentnost'. Chtoby ispol'zovat' podobnye ustroistva dlya simulyatsii proizvol'nogo vida gamil'tonianov, neobkhodimo stroit' priblizheniya, pozvolyayushchie s pomoshch'yu dostupnykh operatsii vosproizvesti proizvol'nyi operator evolyutsii i pri etom ispol'zuyushchie kak mozhno men'she obrashchenii k kvantovomu ustroistvu.

Izvestno neskol'ko printsipial'no razlichnykh algoritmov postroeniya podobnykh priblizhenii, i v dannom obzore my rassmotrim naibolee aktivno izuchaemye:

• metod Suzuki-Trotter, osnovannyi na khoroshem priblizhenii eksponenty ot summy ermitovykh operatorov cherez eksponenty ot kazhdogo iz chlenov summy,
• pryamoe razlozhenie eksponenty operatora evolyutsii v ryad Teilora po vremeni evolyutsii,
• metod Quantum Signal Processing, osnovannyi na effektivnom metode simulyatsii polinomov ot zadannogo ermitovogo operatora, chto zatem ispol'zuetsya dlya polinomial'noi approksimatsii eksponenty ot operatora evolyutsii.

Razvitie tekhnologii proizvodstva i izmereniya sverkhprovodyashchikh kubitov v Rossii uzhe pozvolyaet sozdavat' mnogokubitnye svyazannye sistemy, iz kotorykh mozhno delat' razlichnye analogovye i tsifrovye simulyatory. Poluchennyi v sozdanii dvukhkubitnykh geitov opyt pokazal nam napravlenie dlya dal'neishego razvitiya v etoi sfere: kakie tipy geitov neobkhodimo ispol'zovat' i uluchshat', kak vyklyuchat' ostatochnoe ZZ vzaimodeistvie vo vremya prostaivaniya kubitov. Ya predstavlyu nashi rezul'taty i rasskazhu o potentsial'nykh sposobakh prodvizheniya v etikh oblastyakh.

In the talk, we focus on the physics of magneto-excitons in a quantum Hall insulator at the filling factor of 2. The simplest realizations are magneto-excitons formed by an electron promoted from the occupied zeroth Landau level to the empty first Landau level and by the vacancy under the Fermi level. There are two magneto-excitons: a spin-singlet with total spin S = 0; and a spin-triplet (CSFE) with total spin S = 1. The first one is magneto-plasmon which decays with the emission of a photon. In contrast, the CSFE is not radiatively active owing to electron spin conservation and its energy is lower than the cyclotron energy. Consequently, spin-triplet magneto-excitons exhibit relaxation time reaching up to 900 us. We also discovered condensation of excitons by measurement of exciton lifetime in a temperature range of 0.5–1.5 K. Here we report on spin exciton transfer at distance exceeding 200 μm by pump-probe photo-luminescence measurements and photo-resonant reflection. These effects exhibit threshold both in excitation power and temperature.

The experimental studies on CSFE ensembles that have to obey the Bose-Einstein statistics signal the emergence of an excitonic coherent phase. In the present paper, the theory is developed of the weakly interacting Bose gas of spin-cyclotron excitations in terms of a virial correction to the single magnetoexciton energy. The condition for a coherent-incoherent phase transition is discussed. It is expected to be strongly related to the studied long-distant inter-excitonic correlations. The results obtained theoretically are discussed in terms of their agreement with specific experimental data.

Effekt blizosti v gibridnykh sistemakh sverkhprovodnik-normal'nyi metall okazyvaet sushchestvennoe vliyanie na kogerentnye kolebaniya sverkhprovodyashchego parametra poryadka Δ, izvestnye kak mody Khiggsa. Standartnaya moda Khiggsa s chastotoi 2Δ ispytyvaet zatukhanie iz-za utechki kvazichastits iz sverkhprovodnika v normal'nyi metall. Pomimo etogo iz-za kogerentnogo tunnelirovaniya elektronov mezhdu sverkhprovodnikom i normal'nym metallom poyavlyayutsya dve dopolnitel'nye khiggsovskie mody s chastotami, opredelyaemymi pervichnoi shchel'yu Δ i navedennoi shchel'yu v normal'nom metalle. Eti tri mody opredelyayut asimptoticheskoe povedenie sverkhprovodyashchego parametra poryadka, vozmushchennogo elektromagnitnym impul'som libo rezkim izmeneniem parametrov sistemy. Issledovanie mod Khiggsa v gibridnykh strukturakh vazhno dlya ponimaniya dinamicheskikh svoistv sverkhprovodyashchikh priborov, osnovannykh na effekte blizosti.

Kvantovye vychisleniya v poslednee vremya yavlyayutsya aktivno razvivayushcheisya oblast'yu prikladnoi fiziki i teorii informatsii. Odnim iz mnogoobeshchayushchikh primenenii vozmozhnostei segodnyashnikh kvantovykh komp'yuterov yavlyayutsya kvantovyi simulyatsii fizicheskikh sistem na sistemakh kubitov. Odnako, sushchestvennymi problemami na puti k fizicheski korrektnym simulyatsiyam yavlyayutsya trotterovskaya oshibka diskretizatsii i razlichnye effekty shuma. V etom doklade budet predlozhena prostaya tochno reshaemaya model' sistemy spinov, pozvolyayushchaya izuchit' osnovnye effekty trotterovskoi oshibki i dayushchaya vozmozhnost' dlya izucheniya effektov shuma.

We determine the noise of charge current that is generated by a precessing magnetization of a small itinerant ferromagnet, which is driven by ferromagnetic resonance (FMR) and tunnel-coupled to two normal metal leads. Even when the leads are in equilibrium with each other, i.e. neither voltage nor thermal bias is applied, the electron system is driven out of equilibrium by the precessing magnetization. In turn, a non-equilibrium electron distribution develops in the small ferromagnet. This distribution is governed by the dynamics of the magnetization and determines the (zero-frequency) noise of charge current. We show that this noise can be used to gain information about the magnetization dynamics.

(po motivam izucheniya stat'i A.Yu. Kitaeva)

Postroena teoriya, opisyvayushchaya vzaimodeistvie elektromagnitnogo polya s drozhashchei dispergiruyushchei sredoi. V pervom poryadke po mekhanicheskomu smeshcheniyu vychislena popravka k polyarizuemosti sredy, obuslovlennaya drozhaniem. Pokazano, chto dvizhenie v prostranstve elektricheskogo dipolya privodit k poyavleniyu magnitnogo dipol'nogo i elektricheskogo kvadrupol'nogo momentov. Teoriya primenena dlya opisaniya neuprugogo rasseyaniya sveta na drozhashchikh chastitsakh i membranakh. Ustanovleno, chto kharakter interferentsii elektromagnitnykh voln, izluchennykh razlichnymi mul'tipolyami, opredelyaetsya chastotnoi zavisimost'yu dielektricheskoi pronitsaemosti. V sluchae, kogda ona imeet rezonans, vblizi nego svet rasseivaetsya preimushchestvenno vpered, a vdali ot nego — nazad. Takzhe opisana konversiya polyarizatsii sveta v protsesse neuprugogo rasseyaniya.

A. V. Poshakinskiy and A. N. Poddubny, Phys. Rev. X 9, 011008 (2019).

V doklade budet obsuzhdat'sya zadacha ob anomal'nom skeilinge v turbulentnosti. Eto yavlenie proyavlyaetsya v singulyarnom (vozmozhno stepennom) povedenii razlichnykh statisticheskikh velichin, zavisyashchikh ot integral'nogo masshtaba turbulentnosti s beskonechnym kolichestvom nezavisimykh anomal'nykh pokazatelei. I eksperimenty, i chislennoe modelirovanie pokazyvayut, chto otkloneniya ot klassicheskoi teorii Kolmogorova bolee yarko vyrazheny dlya passivnogo perenosa skalyarnykh polei (naprimer, polya temperatury ili plotnosti primesi), chem dlya samogo polya skorosti. Samyi znachitel'nyi progress byl dostignut dlya modeli Kreichnana, gde pole skorostei perenosa yavlyaetsya gaussovym, ne korrelirovannym po vremeni. V protsesse doklada budet podrobno obsuzhdat'sya metod renormgruppy v primenenii k etoi modeli, a takzhe k bolee slozhnym i realistichnym modelyam perenosa.

V ramkakh diagrammnoi tekhniki vyvoditsya analiticheskoe vyrazhenie dlya dispersii kondaktansa neuporyadochennogo obraztsa cherez propagatory, podchinyayushchiesya transportnomu uravneniyu. Vychisleniya osnovany na sootnosheniyakh dlya vershiny Khikami bez ispol'zovaniya diffuzionnogo (gradientnogo) razlozheniya i bornovskogo priblizheniya dlya odnotsentrovogo rasseyaniya. Obsuzhdayutsya prichiny usileniya fluktuatsii pri perekhode ot kvaziballisticheskogo k diffuzionnomu rezhimu transporta.

Issledovana dinamika plazmonnogo lazera s raspredelennoi obratnoi svyaz'yu (DFB lazera) na osnove dvumernoi perforirovannoi metallicheskoi plenki. Dlya takoi struktury mozhno vydelit' dva kharakternykh tipa mod. K pervomu iz nikh otnosyatsya mody, chastota kotorykh nakhoditsya v razreshennoi zone, imeyushchie bol'shie izluchatel'nye poteri i vysokii porog generatsii (svetlye mody). Ko vtoromu tipu otnosyatsya mody, chastota kotorykh nakhoditsya na krayu razreshennoi zony, imeyushchie nizkie izluchatel'nye poteri i nizkii porog generatsii (temnye mody). Pokazano, chto kogda pyatno nakachki men'she razmera poverkhnosti DFB lazera, nelineinoe vzaimodeistvie mezhdu modami periodicheskoi plazmonnoi struktury cherez aktivnuyu sredu privodit k novomu effektu, a imenno k kooperatsii mod [1]. Kooperatsiya mod proyavlyaetsya kak generatsiya svetlykh mod s vysokimi poteryami vmesto generatsii temnykh mod s nizkimi poteryami. Pokazano, chto etot effekt imeet mesto v dvumernykh DFB lazerakh i ne proyavlyaetsya v odnomernykh DFB lazerakh. Vzaimodeistvie svetlykh mod voznikaet iz-za neortogonal'nosti lazernykh mod v oblasti nakachki, gde svetlye mody stanovyatsya sinkhronizirovannymi po faze. Kak sledstvie, voznikaet ikh konstruktivnaya interferentsiya. Prodemonstrirovano, chto vsledstvie kooperatsii mod imeet mesto ushirenie diagrammy napravlennosti vyshe poroga generatsii, chto nablyudalos' v nedavnikh eksperimentakh [2].

[1] N.E. Nefedkin, A.A. Zyablovsky, E.S. Andrianov, A.A. Pukhov, and A. P. Vinogradov, ACS Photonics 2018 5(8): p. 3031-3039.
[2] Tenner, V.T., M.J.A. de Dood, and M.P. van Exter, Measurement of the phase and intensity profile of surface plasmon laser emission. ACS Photonics, 2016. 3: p. 942−946.

V doklade budet predstavlen odin iz metodov dlya opisaniya gidrodinamicheskikh plazmennykh effektov v dvumernykh elektronnykh sistemakh (DES). A imenno, budet primenen operatornyi podkhod k uravneniyam elektronnoi gidrodinamiki i postroen analog kvantovo-mekhanicheskoi teorii vozmushchenii. Razrabotannaya teoriya pozvolit poluchit' vyrazhenie dlya pervoi popravki k sobstvennoi chastote plazmonov v prisutstvie slabogo dreifa nositelei, magnitnogo polya, vyazkosti i rasseyaniya na primesyakh. Na model'nykh primerakh budet vyyavlen kharakter vliyaniya etikh vozmushchenii na spektr i ustoichivost' plazmennykh voln v razlichnykh strukturakh. Tak, budut opredeleny: (1) obshchie svoistva tokovykh neustoichivostei v ogranichennykh DES, (2) vliyanie dreifa nositelei na spektr plazmonov v periodicheskikh DES (usilennyi effekt Doplera), i (3) mekhanizmy vozbuzhdeniya kraevykh mod postoyannym tokom.

Razvita teoriya opticheskoi spektroskopii neravnovesnykh spinovykh i zaryadovykh fluktuatsii v kvantovoi tochke, pomeshchennoi v mikrorezonator. Pokazano, chto v rezhime sil'noi svyazi fotonnoi mody mikrorezonatora s trionnym rezonansom kvantovoi tochki fluktuatsii koeffitsienta prokhozhdeniya sveta cherez mikrorezonator soderzhat informatsiyu kak o spinovoi dinamike sistemy, tak i o statistike fotonov v mikrorezonatore. V rezhime slaboi svyazi vozmozhno formirovanie "odetykh fotonami" sostoyanii, chto pozvolyaet opredelyat' parametry spinovoi spinovoi dinamiki ne tol'ko dlya osnovnogo, no i dlya vozbuzhdennogo sostoyaniya kvantovoi tochki po fluktuatsiyam opticheskikh signalov Faradeya ili Kerra. Prilozhenie k sisteme prodol'nogo magnitnogo polya privodit k vozmozhnosti detektirovaniya zaryadovykh fluktuatsii v kvantovoi tochke.

This will include e.g. works like
[1] R. Klees, G. Rastelli, J.C. Cuevas, and W. Belzig, "Quantum Geometry of Josephson Matter" (submitted to Science Advances, not on arxiv yet).
[2] Tomohiro Yokoyama, Johannes Reutlinger, Wolfgang Belzig, and Yuli V. Nazarov, "Order, disorder and tunable gaps in the spectrum of Andreev bound states in a multiterminal superconducting device", Phys. Rev. B 95, 045411 (2017) [arXiv:1609.05455].
[3] J. Reutlinger, L. Glazman, Yu. V. Nazarov, and W. Belzig, ""Smile" gap in the density of states of a cavity between superconductors", Phys. Rev. Lett. 112, 067001 (2014) [arXiv:1308.2529].

Presentations: 1.QuantumGeomJJ.pdf, 2.SmileTopo.pdf

Recent measurements of the conductivity of nanoperforated graphene are interpreted in terms of edges states existing near the edge of each nanohole. The perimetric quantization of edge states should result in the formation of a quasi-equidistant ladder of quasistationary energy levels. Dirac fermions filling this ladder rotate about each nanohole in the direction determined by the valley index. We show that the irradiation of this system by circularly polarized terahertz radiation leads to a resonance in absorption in one of the valleys. The magnitude of absorption at the resonance frequency can be controlled by means of gate voltage.

Izucheno dvizhenie elektrona v membrane pod vliyaniem ravnovesnykh izgibnykh kolebanii, korrelyator kotorykh ubyvaet s rasstoyaniem po zakonu r^{-2\eta}. Podrobno rassmotren sluchai \eta<1/2, kogda dazhe pri skol' ugodno slabom vzaimodeistvii teoriya vozmushchenii neprimenima. Pokazano, chto v etom sluchae obratnoe kvantovoe vremya proportsional'no g^{1/(1-\eta)} T^{(2-\eta)/(2-2\eta)}, gde g - konstanta elektron-fononnogo vzaimodeistviya, a T - temperatura. Razvityi metod prilozhen k vychisleniyu plotnosti sostoyanii elektrona v perpendikulyarnom k membrane magnitnom pole. Pokazano, v chastnosti, chto v rezhime slaboushirennykh besporyadkom urovnei Landau oni imeyut gaussovu formu s shirinoi, zavisyashchei ot magnitnogo polya po zakonu B^\eta. Krome togo, vychisleno vremya sboya fazy volnovoi funktsii elektrona za schet ego vzaimodeistviya s izgibnymi fononami v sluchae \eta<1/2. Pokazano, chto imeetsya neskol'ko temperaturnykh intervalov, v kotorykh vremya sboya fazy vyrazhaetsya razlichnymi stepennymi funktsiyami ot konstanty elektron-fononnogo vzaimodeistviya, temperatury i energii elektrona.

We describe theoretically the depairing effect of a microwave field on diffusive s-wave superconductors. The ground state of the superconductor is altered qualitatively in analogy to the depairing due to a dc current. In contrast to dc-depairing the density of states acquires, for microwaves with frequency \omega_0, steps at multiples of the photon energy \Delta \pm n\hbar\omega_0 and shows an exponential-like tail in the subgap regime. We show that this ac-depairing explains the measured frequency shift of a superconducting resonator at high microwave power and low temperatures.

Kvantovyi turniket predstavlyaet soboi nanoelektronnoe ustroistvo, kontroliruemym obrazom perenosyashchee elektrony po odnomu mezhdu dvumya sverkhprovodyashchimi elektrodami putem podachi peremennogo napryazheniya na metallicheskuyu nanochastitsu, raspolozhennuyu mezhdu dvumya elektrodami. Okazyvaetsya, chto kogerentnaya svyaz' mezhdu elektronnymi sostoyaniyami v nanochastitse i kvazichastichnymi sostoyaniyami v sverkhprovodnikakh nakladyvaet fundamental'nye ogranicheniya na rabotu ustroistva.

Referativnyi doklad po rabote D. M. Silevitch, T. F. Rosenbaum and G. Aeppli, Eur. Phys. J. Special Topics 224, 25 (2015)

Traditional simulated annealing uses thermal fluctuations for convergence in optimization problems. Quantum tunneling provides a different mechanism for moving between states, with the potential for reduced time scales and different outcomes. Thermal and quan- tum annealing are compared in two concentration regimes of a model disordered magnet, where the effects of quantum mechanics can be tuned both by varying an applied magnetic field and by controlling the strength of thermal coupling between the magnet and an external heat bath. The results indicate that quantum annealing hastens convergence to the final state, and that the quantum character of the final state can be engineered thermodynamically.

Referativnyi doklad po rabote V. S. Denchev et al (Google Inc.), arxiv.org/1512.02206

Quantum annealing (QA) has been proposed as a quantum enhanced optimization heuristic exploiting tunneling. Here, we demonstrate how finite range tunneling can provide considerable computational advantage. For a crafted problem designed to have tall and narrow energy barriers separating local minima, the D-Wave 2X quantum annealer achieves significant runtime advantages relative to Simulated Annealing (SA). For instances with 945 variables, this results in a time-to-99%-success-probability that is ∼108 times faster than SA running on a single processor core. We also compared physical QA with Quantum Monte Carlo (QMC), an algorithm that emulates quantum tunneling on classical processors. We observe a substantial constant overhead against physical QA: D-Wave 2X again runs up to ∼108 times faster than an optimized implementation of QMC on a single core. We note that there exist heuristic classical algorithms that can solve most instances of Chimera structured problems in a timescale comparable to the D-Wave 2X. However, we believe that such solvers will become ineffective for the next generation of annealers currently being designed. To investigate whether finite range tunneling will also confer an advantage for problems of practical interest, we conduct numerical studies on binary optimization problems that cannot yet be represented on quantum hardware. For random instances of the number partitioning problem, we find numerically that QMC, as well as other algorithms designed to simulate QA, scale better than SA. We discuss the implications of these findings for the design of next generation quantum annealers.

Out-of-time-order correlators introduced recently in the context of quantum gravity describe the delocalization of information in quantum systems. In classical chaotic systems, these correlators are known to grow exponentially with the Lyupanov exponent. I discuss the behavior of these correlators in canonical examples of solid state quantum chaotic systems: disordered electrons with and without phonon interaction.

We explore a long Josephson contact transporting Cooper pairs between 1D charge-neutral chiral Majorana modes in the leads via charged Dirac chiral modes in the normal region. We investigate the regimes of transparent and tunnel junctions implemented in 3D topological insulator/superconductor/magnet hybrid structures. The setup acts as a SQUID controlled by the magnetic flux enclosed by the chiral loop of the normal region. This chirality leads to the fractional h/e-periodic pattern of critical current. The current-phase relation can have sawtooth-like shape with spikes at unusual even phases of 2\pi n.

Referativnyi doklad po rabote Cecile Monthus, arxiv:1510.08322.

V rabote teoreticheski pokazano, chto kriticheskii tok dzhozefsonovskogo kontakta, soderzhashchego nanoprovoloku s dvumya provodyashchimi kanalami, ispytyvaet mnogoperiodicheskie magnitnye ostsillyatsii. Mnogoperiodichnost' voznikaet iz-za kvantovomekhanicheskoi interferentsii mezhdu kanalami, na kotoruyu sushchestvennoe vliyanie okazyvayut sil'nye spin-orbital'noe i zeemanovskoe vzaimodeistviya. Rassmotrennaya minimal'naya dvukhkanal'naya model' pozvolyaet ob'yasnit' slozhnye interferentsionnye yavleniya, obnaruzhennye v eksperimentakh po izmereniyu dzhozefsonovskogo transporta cherez nanoprovoloki vismuta.

Referativnyi doklad po rabote Y.-C. He, S. Bhattacharjee, F. Pollmann, R. Moessner, arXiv:1509.03070

Referativnyi doklad pro vozmozhnuyu realizatsiyu topologicheskogo izolyatora v sil'nokorrelirovannoi elektronnoi sisteme. Teoreticheskoe predskazanie i eksperimental'nye svidetel'stva v materiale SmB_6.

[1] M. Dzero, K. Sun, V. Galitski, P. Coleman, PRL 104, 106408 (2010).
[2] M. Ye, J. W. Allen, K. Sun, http://arxiv.org/abs/1307.7191
[3] S. Wolgast, Ç. Kurdak, K. Sun, J. W. Allen, D.-J. Kim, Z. Fisk, PRB 88, 180405(R) (2013).

My izuchaem tokovyi shum v CdHgTe/HgTe/CdHgTe kvantovoi yame s invertirovannoi zonnoi strukturoi v rezhime neuporyadochennogo kraevogo transporta. V soglasii s predydushchimi eksperimentami soprotivlenie kraya sushchestvenno prevoskhodit h/e2 i slabo zavisit ot temperatury. Drobovoi shum v rezhime kraevogo transporta znachitel'no podavlen po sravneniyu s puassonovskim znacheniem i kharakterizuetsya faktorom Fano v diapazone 0.1 < F < 0.3 dlya razlichnykh obraztsov i znachenii zatvornogo napryazheniya. S uchetom togo, chto dlina kraya men'she ballisticheskoi dliny sboya fazy, eti nablyudeniya isklyuchayut vozmozhnost' odnomernogo gelikal'nogo kraevogo transporta v nashikh obraztsakh. Rezul'taty eksperimenta kachestvenno mozhno ob'yasnit' v modeli neuporyadochennogo mnogokanal'nogo kvazi-odnomernogo transporta vdol' kraya.

Vychisleno transportnoe sechenie rasseyaniya elektronov v grafene na kruglom otverstii (ili defekte). Predpolagaetsya, chto na krayu otverstiya mogut sushchestvovat' kvazistatsionarnye kraevye (tammovskie) sostoyaniya, kotorye privodyat k pikam v sechenii rasseyaniya, kotorye mogli nablyudat'sya v transportnykh eksperimentakh [Yu.I. Latyshev i dr., Pis'ma v ZhETF 98, 242 (2013), Yu.I. Latyshev et al., Scientific Reports 4, 7578 (2014)]. Obsuzhdaetsya uchet neodnorodnosti kraya, a takzhe zaryazhennosti nanootverstiya (defekta), chto privodit k razmytiyu i smeshcheniyu pikov.

The concept of the odd-frequency Cooper pairs was first proposed by Berezinskii in 1974 to describe superfluidity of 3He [1]. Although the odd-frequency superconductivity has never been confirmed in any materials, the odd-frequency pairs appear as the subdominant pairing correlation in various proximity structures such as superconductor / ferromagnet (SF) junctions [2] and normal-metal / superconductor (NS) junctions with unconventional pairing symmetry [3]. In the presentation, we explain what the odd-frequency pairs are, how they appear in such proximity structure, how to detect them, and how they are different from usual even-frequency pairs in the bulk. We first discuss the enhancement of the quasiparticle density of states at the zero-energy [2,4-5] and its influence on the low-energy electric transport [6]. Next we show the paramagnetic property of odd-frequency pairs [7-10] which can be confirmed in the surface impedance measurement at low temperature [11]. We also discuss a relation to the Majorana physics [12-13]. Finally we explain why such unusual pairs appear in inhomogeneous superconducting systems [14].

[1] V. L. Berezinskii, JETP Lett. 20, 287 (1974). [2] F. S. Bergeret, A. F. Volkov, and K. B. Efetov, Phys. Rev. Lett. 86, 4096 (2001) [3] Y. Tanaka and A. A. Golubov, Phys. Rev. Lett. 98, 037003 (2007). [4] Y. Asano, Y. Tanaka, and A. A. Golubov, Phys. Rev. Lett.98, 107002 (2007). [5] T. Kontos, et. al. Phys. Rev. Let. 86, 304 (2001). [6] Y. Asano, et. al., Phys. Rev. Lett. 99, 067005 (2007). [7] H. Walter, et. al., Phys. Rev. Lett. 80, 3598 (1998). [8] S. Higashitani, J. phys. soc. Jpn., 66, 2556 (1997). [9] S.-I. Suzuki and Y. Asano, Phys. Rev. B 89, 184508 (2014). [10] Y. Tanaka, et. al., Phys. Rev. B 72, 140503(R) (2005). [11] Y. Asano, et. al,, Phys. Rev. Lett. 107, 087001 (2011). [12] Y. Asano and Y. Tanaka, Phys. Rev. B 87, 104513 (2013). [13] S. Ikegaya, Y. Asano, and Y. Tanaka, arXiv: 1411.3438 [14] Y. Asano, Y. V. Fominov, Y. Tanaka, Phys. Rev. B 90, 094512 (2014).

The unconventional (half-integer) quantum Hall effect for a single species of Dirac fermions is analyzed. In the introduction I will discuss experimental measurements of the half-integer Hall conductance g_{xy} of topological insulator surface states and unveil its field theoretical origin. For the calculation of the conductivity tensor, the following two step procedure is applied. In the first step, semiclassical transport coefficients are derived in the case of both orbital and Zeeman coupling to an external magnetic field. In this context, I plan to give a pedagogic review of the modified Boltzmann transport theory for the anomalous Hall effect. The semiclassical conductivity tensor serves as input parameters for the second step: It consists in the renormalization group treatment of the appropriately modified non-linear sigma model and thus accounts for localization effects. The resulting phase diagram (levitation scenario) will also be discussed in this context. If time permits, I will further explain how to reconcile Laughlin's flux insertion argument with half-integer Hall conductance and/or present the calculation of the current density beyond linear response in the limit of smooth scalar potential.

Obychno schitaetsya, chto v topologicheskikh izolyatorakh (TI) spektr poverkhnostnykh sostoyanii imeet besshchelevoi lineinyi (ul'trarelyativistskii) spektr v tsentre zony Brillyuena. Takoi spektr deistvitel'no poluchaetsya v prosteishikh modelyakh pri ispol'zovanii “otkrytykh granichnykh uslovii” (open boundary conditions) [X.-L. Qi, S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)], t.e. granichnykh uslovii zanulyayushchikh volnovuyu funktsiyu na granitse. Odnako, izvestno, chto effektivnaya volnovaya funktsiya, opisyvayushchaya elektrony v kristalle, ne obyazana zanulyat'sya na granitse [E.L. Ivchenko “Optical Spectrosopy of Semiconductor Nanostructires”, Alpha Science, Harrow, UK (2005) i ssylki v nei]. Teoriya TI, a tochnee “printsip sootvetstviya granitsa-ob'em” (bulk boundary correspondence) predskazyvaet nalichie kraevykh sostoyanii v ob'emnoi shcheli, no ne sam spektr, kotoryi dolzhen zaviset' ot svoistv i mikrostruktury poverkhnosti, chto ne uchityvaetsya otkrytymi granichnymi usloviyami. V nashei rabote arXiv:1407.0945 byli proanalizirovany vozmozhnye granichnye usloviya v 2D TI na osnove kvantovykh yam CdHgTe i v 3D TI Bi2Se3. Pokazano, chto poverkhnostnye sostoyaniya mogut imet' sushchestvenno ne lineinyi spektr ili vovse otsutstvovat' v tsentre zony Brillyuena.

My rassmatrivaem sistemu provodnikov, pomeshchennykh v dielektricheskuyu matritsu. Matritsa ne predpolagaetsya sovershenno zhestkoi (naprimer, eto mozhet byt' zhidkost'), poetomu tolshchiny dielektricheskikh zazorov mezhdu provodnikami fluktuiruyut vo vremeni i inogda provodniki mogut soprikasat'sya. V takie momenty voznikaet "proboi" i zaryad legko peretekaet mezhdu paroi soprikosnuvshikhsya provodnikov. Protsess perenosa zaryada za schet proboev, voznikayushchikh v sluchainye momenty v sluchainykh mestakh, my nazvali polzuchei provodimost'yu. My rassmatrivaem kak trekhmernye, tak i nizkorazmernye massivy provodnikov i issleduem rastekanie zaryada, pervonachal'no sosredotochennogo na odnom provodnike, provodimost' na postoyannom toke, fluktuatsii zaryadov na provodnikakh i ikh prostranstvenno-vremennuyu korrelyatsiyu.

Obzor rabot

Nature 505, 528 (2014) Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state, A F Young, J D Sanchez-Yamagishi, B Hunt, S H Choi, K Watanabe, T Taniguchi, R C Ashoori and P Jarlillo-Herrero,

Nat Phys 8, 550 (2012) Spin and valley quantum Hall ferromagnetism in graphene, A F Young, C R Dean, L Wang, H Ren, P Cadden-Zimansky, K Watanabe, T Taniguchi, J Hone, K L Shepard and P Kim

We study transport via edge modes of a 2D topological insulator. Topological protection prevents complete localization of the edge states; however, quantum interference effects are still relevant for the transport properties at finite length scales. We mainly focus on the two most experimentally relevant cases: (i) a junction between two quantum Hall insulators with different filling factors and hence an imbalance in the number of right- and left-propagating modes (symmetry class A) and (ii) a relatively thick HgTe quantum well in the insulating state with an arbitrary number of edge modes (symmetry class AII). We derive the distribution of transmission probabilities as a function of the distance between leads. This allows us to demonstrate topological effects in the average conductance and the shot noise of the setup. We also consider mesoscopic fluctuations and compute the variance of conductance. This quantity is strongly influenced by topology in the quantum Hall case. All the calculations are carried out assuming localization effects are weak, i.e., in the short length limit. Technically, this amounts to studying 1D non-linear sigma model with a proper topological term and source fields on the semiclassical level. Remarkably, the semiclassical limit of the 1D sigma model can be exactly mapped onto a fully quantum 0D sigma model of a different symmetry class. This allows us to identify the distribution of transmission probabilities with the spectrum of a certain random matrix.

Rabota posvyashchena izgotovleniyu submikronnykh planarnykh S-N-S dzhozefsonovskikh kontaktov, planarnykh gibridnykh struktur na osnove sverkhprovodnika, normal'nogo metalla i ferromagnetika, eksperimental'nomu issledovaniyu osobennostei effekta blizosti i sverkhprovodyashchego transporta cherez takie struktury, realizatsii S-(N/F)-S - dzhozefsonovskogo kontakta s ferromagnitnym monodomennym podsloem (F), issledovaniyu vliyaniya ferromagnitnogo podsloya na parnyi i kvazichastichnyi transport cherez dzhozefsonovskii S-(N/F)-S kontakt, izucheniyu nelokal'nykh neravnovesnykh effektov v mnogoterminal'nykh SNS strukturakh, svyazannykh s inzhektsiei kvazichastits v odin iz beregov dzhozefsonovskogo S-N-S kontakta.

Predstavleny rezul'taty issledovaniya atomno-chistoi poverkhnosti topologicheskogo izolyatora Bi2Se3 metodami sverkhvysokovakuumnoi nizkotemperaturnoi skaniruyushchei tunnel'noi mikroskopii (STM) i spektroskopii (STS). Obnaruzheny defekty glubina zaleganiya i ozhidaemyi zaryad kotorykh sootvetstvuet r-tipu provodimosti ob'ema kristalla. Znak termo-eds takzhe sootvetstvuet r-tipu provodimosti. Rezul'taty issledovanii metodami tunnel'noi spektroskopii pokazyvayut, chto uroven' khimicheskogo potentsiala nakhoditsya vnutri zapreshchennoi zony ob'ema. Obnaruzheno izmenenie lokal'noi plotnosti sostoyanii vblizi kraya pyatisloinoi stupeni, kotoroe sootvetstvuet sdvigu polozheniya vershiny dirakovskogo konusa otnositel'no ob'emnoi zony ili zhe takzhe sdvigu khimicheskogo potentsiala vblizi kraya stupeni.

po rabote A.Yu. Dmitriev et al., http://arxiv.org/abs/1408.4991

We study electronic properties of AA-stacked bilayer graphene. In the single-particle approximation such a system has one electron band and one hole band crossing the Fermi level. If the bilayer is undoped, the Fermi surfaces of these bands coincide. Such a band structure is unstable with respect to a set of spontaneous symmetry violations. Specifically, strong on-site Coulomb repulsion stabilizes antiferromagnetic order. At small doping and low temperatures, the homogeneous phase is unstable and experiences phase separation into an undoped antiferromagnetic insulator and a metal. The metallic phase can be either antiferromagnetic (commensurate or incommensurate) or paramagnetic depending on the system parameters. We derive the phase diagram of the system on the doping-temperature plane and find that under certain conditions, the transition from the paramagnetic to the antiferromagnetic phase may demonstrate reentrance. The application of the transverse voltage induces the exciton order parameter coexisting with antiferromagnetism. The value of this second order parameter is proportional to the biased voltage and the value of the nearest- neighbor inter-plane Coulomb repulsion.

We study the effects of strong coupling of a localized state charge to one-dimensional electronic channels out of equilibrium. While the state of this charge and the coupling strength determine the scattering phase shifts in the channels, the non-equilibrium partitioning noise induces the tunneling transitions to the localized state. The strong coupling leads to a non-perturbative backaction effect which is manifested in the orthogonality catastrophe and the Fermi edge singularity in the transition rates. The non-Gaussian component of noise brakes the charge symmetry, shifting the position of the tunneling resonance depending on the sign of the dissipative current and the transparency of the noise emitting partitioning quantum point contact.

Predlozhen novyi pokhod k resheniyu uravnenii Richardsona-Godena, kotorye opredelyayut sobstvennye sostoyaniya gamil'toniana teorii Bardina-Kupera-Shriffera (BKSh). Vmesto neposredstvennogo resheniya etikh uravnenii mozhno pereiti k veroyatnostnomu predstavleniyu i zatem rekonstruirovat' polozheniya kornei etikh uravnenii na kompleksnoi ploskosti, ispol'zuya metody integrirovaniya. Pri etom voznikayut integraly sel'bergovskogo tipa, figuriruyushchie v konformnoi teorii polya i teorii sluchainykh matrits. V rabote provedeny analiticheskie raschety dlya nizkoenergeticheskoi chasti spektra sistemy v termodinamicheskom predele, dlya kotorogo podtverzhdeno soglasie so srednepolevymi predskazaniyami BKSh. Takzhe predstavleny nekotorye rezul'taty dlya sistem proizvol'nogo razmera, dlya chego byla privlechena ideya o simmetrii mezhdu parami elektronov i parami dyrok. Veroyatnostnyi podkhod mozhet byt' polezen i dlya resheniya drugikh tipov uravnenii Bete.

My eksperimental'no issledovali transport cherez interfeis mezhdu ferromagnetikom (permalloi) i kraem dvumernoi elektronnoi sistemy s sil'nym spin-orbital'nym vzaimodeistviem tipa Rashby. My obnaruzhili sil'no nelineinye transportnye kharakteristiki v oblasti malykh tokov pri millikel'vinovykh temperaturakh. Obnaruzhennaya nelineinost' polnost'yu podavlyaetsya pri dostizhenii nekotorykh znachenii temperatury, magnitnogo polya ili toka cherez interfeis. My interpretiruem dannoe povedenie kak rezul'tat spinovoi akkumulyatsii vblizi interfeisa i ee absorbtsii, vyzvannoi protekayushchim tokom (magnetization torque).

Using the combination of analytical and numerical techniques we develop the theory of quantum criticality in disordered topological multi-channel nanowires of symmetry classes AIII and BDI [1]. The minimal representative phase portrait is characterized by two parameters $(\mu, w)$, where $\mu$ is the external control parameter (e.g. the chemical potential) and $w$ is the disorder strength. With the increase of $w$ at a fixed value of $\mu$ the wires generically undergo a sequence of topological phase transitions before the asymptotic state of a trivial Anderson insulator is reached. The universal description of the systems is given in terms of two parameters $(g,\chi)$, where $g$ is conductance and $\chi$ is a topological angle. Contour lines of half-integer valued $\chi$ in $(\mu, w)$-parameter space define phase boundaries between distinct topological sectors. Upon increasing the length of the wire, the pair $(g, \chi)$ exhibits flow similar to the celebrated two parameter flow describing the class A quantum Hall insulator. However, unlike the quantum Hall system, an exact analytical description of the entire phase diagram can be given. We corroborate the quantitative validity of our theory by comparison to numerical transfer matrix computations.

[1] A. Altland, D. Bagrets, L. Fritz, A. Kamenev, H. Schmiedt, arXiv:1402.1738

Budet dana klassifikatsiya razlichnykh predel'nykh sluchaev, svyazannykh s sootnosheniyami mezhdu integralom mezhsloevogo pereskoka, rasstoyaniem, i shirinoi urovnei Landau. V kazhdom predel'nom sluchae budut ukazany metod vychisleniya mezhsloevoi provodimosti v sil'no anizotropnykh kvazidvumernykh metallakh, oblast' primenimosti etogo metoda, i glavnye rezul'taty etikh raschetov.

[*] P. D. Grigoriev, "Longitudinal interlayer magnetoresistance in quasi-two-dimensional metals", Phys. Rev. B 88, 054415 (2013).

a takzhe
[1] P. D. Grigoriev, «Theory of the Shubnikov-de Haas effect in quasi-two-dimensional metals», Phys. Rev. B 67, 144401 (2003).
[2] P. D. Grigoriev, “Monotonic growth of interlayer magnetoresistance in strong magnetic field in very anisotropic layered metals”, JETP Lett. 94, 47 (2011).
[3] P. D. Grigoriev, “Weakly incoherent regime of interlayer conductivity in magnetic field”, Phys. Rev. B 83, 245129 (2011).
[4] P. D. Grigoriev, M. V. Kartsovnik, W. Biberacher, «Magnetic-field-induced dimensional crossover in the organic metal α-(BEDT-TTF)2KHg(SCN)4», Phys. Rev. B 86, 165125 (2012).
[5] A. D. Grigoriev and P.D. Grigoriev, Crossover from the weak to strong-field behavior of the longitudinal interlayer magnetoresistance in quasi-two-dimensional conductors, Fizika nizkikh temperatur 40(4), 472 (2014).

We present new results on the bistability effect recently observed [Dorozhkin et al., Nature Physics 7, 336 (2011)] in two-dimensional electron systems subjected to the microwave radiation. The effect appears as switching between two states with different electric potential distribution across a sample. Our results here imply that the main difference between these two states is an opposite direction of a long lengthscale electric field which arises spontaneously under conditions when the observable magnetoresistance tends to zero. Although a possibility of the field reversal is an inherent property of states with spontaneously broken symmetry, so far such effect was never observed under stationary external conditions.

V rabote byli issledovany sverkhprovodniki, obladayushchie tripletnym p_x+ip_y tipom sparivaniya, obladayushchie dvukratno vyrozhdennym osnovnym sostoyaniem. Bylo pokazano nalichie fazovogo perekhoda pod deistviem vneshnego magnitnogo polya ili transportnogo toka, snimayushchego dvukratnoe vyrozhdenie i vosstanavlivayushchego Z_2 simmetriyu. Takoi perekhod daet vozmozhnost' dlya upravlyaemoi generatsii domennykh stenok, svyazannykh s narushennoi Z_2 simmetriei osnovnogo sostoyaniya, po mekhanizmu Kibbla-Zureka. Predlozhennyi sposob generatsii domennykh stenok mozhet byt' realizovan v takikh ekzoticheskikh sverkhprovodnikakh kak Sr2RuO4 i v nekotorykh soedineniyakh s tyazhelymi fermionami.

po rabote V. Vadimov, M. Silaev, Phys. Rev. Lett. 111, 177001 (2013)

Budet rasskazano o nedavnikh izmereniyakh sverkhtoka v SNS-kontakte v geterostrukture HgTe/HgCdTe v rezhime kvantovogo spinovogo effekta Kholla [1]. Maksimal'nyi sverkhtok v sisteme izmeren kak funktsiya magnitnogo polya, napravlennogo perpendikulyarno dvumernomu obraztsu, a takzhe zavtornogo napryazheniya, reguliruyushchego plotnost' nositelei v ob'eme. V rezhime, kogda ob'emnye nositeli predpolozhitel'no otsutstvuyut, zavisimost' I(B) imeet priblizitel'no sinusoidal'nyi vid, chto sootvetstvuet sverkhtoku, tekushchemu tol'ko po krayam obraztsa. Period ostsillyatsii sootvetstvuet kvantu potoka Phi_0 cherez kontakt, a amplituda medlenno zatukhaet s rostom magnitnogo polya. Budut obsuzhdeny vozmozhnye prichiny zatukhaniya sverkhtoka, perenosimogo gelikoidal'nymi kraevymi modami.

[1] Molenkamp, Yacoby et al., http://arxiv.org/abs/1312.2559

Rassmatrivaetsya provodyashchee sostoyanie v 2D i 3D topologicheskom izolyatore (TI), tunnel'nym obrazom soedinennom s elektrodami iz normal'nogo metalla. Pokazano, chto kontakty, igraya rol' termostata, vyzyvayut zatukhanie i privodyat k relaksatsii elektronov v TI. Predlozhena prostaya struktura na osnove TI s tunnel'nymi kontaktami, sozdayushchaya chisto spinovyi tok vo vneshnei tsepi. Issleduetsya zavisimost' elektricheskogo i spinovogo toka vo vneshnei tsepi ot sootnosheniya mezhdu kharakternymi dlinami: dlinoi zatukhaniya iz-za tunnelirovaniya, dlinoi kontaktov i, v sluchae 3D TI, dlinoi svobodnogo probega i relaksatsii spina, vyzvannoi rasseyaniem impul'sa na primesyakh.

A number of physical problems may be formulated in terms of non-Hermitian quantum theories. A notable example is provided by mapping of 1D Coulomb gases onto an effective non-Hermitian Quantum Mechanics. Employing methods from algebraic topology we describe a non-perturbative method of instanton calculus for non-Hermitian Hamiltonians. Treating momentum and coordinate as complex variables yields Riemann surfaces of complex energy. The classical and instanton actions are given by the periods of this surface. We demonstrate the accuracy of this analytic procedure in comparison with numerical simulations for a class of periodic non-Hermitian Hamiltonians, as well as the validity of the Bohr-Sommerfeld quantization and Gamow’s formula in these cases.

Recently a new high-mobility Dirac material, trilayer graphene, was realized experimentally. The band structure of ABA-stacked trilayer graphene consists of a monolayer-like and a bilayer-like pair of bands. Here we study electronic properties of ABA-stacked trilayer graphene biased by a perpendicular electric field. We find that the combination of the bias and trigonal warping gives rise to a set of new Dirac points: In each valley, seven species of Dirac fermions with small masses of order of a few meV emerge. The positions and masses of the emergent Dirac fermions are tunable by bias, and one group of Dirac fermions becomes massless at a certain bias value.

Further, we analyze the evolution of the Landau level spectrum as a function of bias. We develop a theoretical model and argue that, in contrast to monolayer and bilayer graphene, the Landau level splittings and quantum Hall phase transitions observed in a recent experiment can be understood within a single-particle picture, but imply the presence of a charge density imbalance between the inner and outer layers of TLG, even at charge neutrality and zero transverse electric field. Our results indicate the importance of a previously unaccounted band structure parameter. We show that the pattern of Landau level crossings is very sensitive to certain band structure parameters, and can therefore provide a useful tool for determining their precise values.

Strong impurities crucially affect the spectral and transport properties of graphene near the Dirac point creating the "mid-gap" states. We first consider the ultimate case of very strong on-site potential impurities that are equivalent to vacancies in the lattice. Vacancies in the honeycomb lattice possess two important properties: (i) they preserve the chiral symmetry of the model and (ii) they scatter resonantly at zero energy (Dirac point). We study the density of states in graphene with sublattice imbalance [1]: we assume that the concentration of vacancies is different in the two sublattices. The imbalance leads to a finite concentration of zero modes of the tight-binding Hamiltonian. We derive the non-linear sigma model for the chiral system with imbalance. Semiclassical density of states acquires a finite gap around the Dirac point with the delta-function peak exactly in the center of the gap. Finite density of zero modes results in the additional term in the sigma-model action. The perturbative renormalization group analysis of this theory yields corrections to the density of states above the gap. In order to obtain a finite density of states below the semiclassical gap, we include non- perturbative contributions to the partition function due to instanton configurations of the field.

Further, we explore the longitudinal conductivity of graphene at the Dirac point in strong magnetic field with two types of short-range scatterers of a finite strength: adatoms that mix the valleys and "scalar" impurities that do not mix them [2]. A scattering theory for the Dirac equation is employed to express the conductance of a graphene sample at charge neutrality as a function of impurity coordinates; an averaging over positions of impurities is then performed numerically. The conductivity is equal to the ballistic value for each disorder realization, provided the number of flux quanta considerably exceeds the number of impurities. For weaker fields, the conductivity in the presence of scalar impurities scales to the quantum-Hall critical point at half filling or to zero away from half filling due to the onset of Anderson localization. For adatoms, the localization behavior is obtained also at half filling due to splitting of the critical energy by intervalley scattering. Our results reveal a complex scaling flow governed by fixed points of different symmetry classes.

[1] E.J. Koenig, I.V. Protopopov, P.M. Ostrovsky, I.V. Gornyi, A.D. Mirlin, and M.A. Skvortsov, in preparation.

[2] S. Gattenloehner, W.-R. Hannes, P. M. Ostrovsky, I. V. Gornyi, A. D. Mirlin, and M. Titov, "Quantum Hall criticality and localization in graphene with short-range impurities at the Dirac point", arXiv:1306.5686.

My eksperimental'no issledovali transportnye svoistva odinochnogo planarnogo kontakta mezhdu niobievym sverkhprovodyashchim elektrodom i kraem dvumernoi elektronnoi sistemy s sil'nym spin-orbital'nym vzaimodeistviem, realizovannoi v uzkoi InGaAs kvantovoi yame. My prodemonstrirovali podavlenie Andreevskogo otrazheniya v oblasti malykh napryazhenii, prilozhennykh k kontaktu, pri sverkhnizkikh temperaturakh (30 mK). Iz analiza temperaturnoi (do 1 K) zavisimosti i zavisimosti ot magnitnogo polya, orientirovannogo v ploskosti dvumernoi sistemy, my interpretiruem obnaruzhennoe podavlenie kak rezul'tat spin-orbital'nogo vzaimodeistviya. Tak zhe, pri opredelennom nabore parametrov, issleduemaya sistema demonstriruet priznaki realizatsii rezhima topologicheskoi sverkhprovodimosti.

arXiv:1305.5685

We consider a bath of fermions in one dimension at zero temperature, and an impurity particle immersed in this bath with some initial momentum. The following questions are addressed: How does the impurity momentum evolve? Does it relax to zero in the long run?

V rabote izuchayutsya mezoskopicheskie fluktuatsii lokal'noi plotnosti sostoyanii okolo perekhoda metall-dielektrik v neuporyadochennoi vzaimodeistvuyushchei elektronnoi sisteme. Pokazano, chto mul'tifraktal'noe povedenie lokal'noi plotnosti sostoyanii vyzhivaet v prisutstvie kulonovskogo vzaimodeistviya. Dlya perekhoda metall-izolyator v prisutstvie kulonovskogo vzaimodeistviya v razmernosti 2+\epsilon vychislen spektr mul'tifraktal'nykh razmernostei, kotoryi okazyvaetsya drugim, chem v sluchae bez vzaimodeistviya.

Doklad po rabote: I.S. Burmistrov, I.V. Gornyi, A.D. Mirlin, "Multifractality at Anderson transitions with Coulomb interaction", arxiv:1305.2888

Teoreticheski izucheno vliyanie slabogo besporyadka na effekt Aaronova-Boma v odnokanal'nykh kvantovykh kol'tsakh s tunnel'nymi kontaktami. Temperatura predpolagaetsya mnogo bol'shei mezhurovnevogo rasstoyaniya v kol'tsakh. V otsutstvie besporyadka zavisimost' kondaktansa kolets ot magnitnogo potoka pri takikh temperaturakh imeet uzkie provaly (antirezonansy). Rassmotreno vliyanie razlichnykh tipov besporyadka na eti antirezonansy. Pokazano, chto korotkodeistvuyushchie primesi privodyat k ushireniyu antirezonansov, odnako ikh glubina ne menyaetsya v shirokom diapazone parametrov. Plavnyi besporyadok privodit k poyavleniyu novykh antirezonansov. Teoriya obobshchaetsya na sluchai, kogda v kol'tsakh pomimo primesei prisutstvuet spin-orbital'noe i zeemanovskoe vzaimodeistvie.

http://arxiv.org/abs/1303.3486

Planiruetsya (i) na dvukh primerakh iz stat. fiziki pokazat', kak mozhet vyglyadet' statistika minimumov gaussova sluchainogo protsessa; (ii) proyasnit' tekushchii matematicheskii status prostykh retseptov vychisleniya khvosta raspredeleniya minimuma; (iii) esli ostanetsya vremya, razobrat' vyvod polnoi statistiki dlya brounovskogo bluzhdaniya s kvadratichnym dreifom ("toy model") -- renormgruppu (Ma-Dasgupty) dlya sil'nogo besporyadka i ekvivalentnost' kvantovoi odnomernoi zadache Izinga v sluchainom poperechnom pole (chast' (iii) po Le Doussal, Monthus 2003).

Metodom chislennogo analiza uravnenii na volnovye funktsii v priblizhenii Khatri-Foka pokazano, chto v standartnoi modeli Andersona na 3-kh mernoi reshetke s on-site disorder pri besporyadke W slegka men'she kriticheskogo znacheniya W_c=16.5, uchet kulonovskogo vzaimodeistviya privodit k fraktal'nomu povedeniyu volnovykh funktsii vblizi urovnya Fermi. Rezul'taty ukazyvayut na vozmozhnost' sushchestvovaniya tseloi promezhutochnoi "kriticheskoi fazy" v nekotoroi polose znachenii kulonovskoi konstanty vzaimodeistviya.

We experimentally demonstrate the simultaneous reconstruction of the bulk and the edge energy spectra caused by strong spin-orbit interaction, at the two lowest filling factors ν=1 and ν=2 for InxGa1−xAs two-dimensional electron system with x=0.75. The observed reconstruction is of different character at these filling factors: It is characterized by zeroing of the energy gap at the levels crossing point at ν=2, while the reconstruction at ν=1 goes through the coexistence of two ν=1 quantum Hall phases with different spin projections. An analysis indicates a strong influence of many-body interaction on the reconstruction at ν=1.

[A. Kononov, G. Biasiol, L. Sorba, and E. V. Deviatov, Phys. Rev. B 86, 125304 (2012)]

It has been recently predicted that Coulomb interaction drives a surface of a 3D topological insulator into a critical state (Ostrovsky et al., PRL 105, 036803 (2010)). We employ the sigma-model formalism to investigate the effect of electron-electron interaction on the transport by surface states in topological insulator thin films. We take into account the interaction of electrons on different surfaces and also the top-bottom asymmetry of the film (different densities of states and strength of disorder on top/bottom surface). This asymmetry is naturally present in experiments where the electronic densities on the surfaces are controlled independently by means of electrostatic gates. The lack of symmetry between top and bottom surfaces is shown to have strong effect on the film conductivity. The interplay of weak antilocalization, Coulomb interaction within and between surfaces and topological protection leads to a rich flow diagram representing the low temperature behavior of the system. In particular, the intersurface interaction is found to evoke a non-monotonic temperature dependence of the conductuctivity and eventually drives the film into a metallic state. The connection with recent experiments on Bi_2Se_3 films is discussed.

We address the problem of a Luttinger liquid with a scatterer that allows for both coherent and incoherent scattering channels. The asymptotic behavior at zero temperature is governed by a new stable fixed point: a Goldstone mode dominates the low energy dynamics, leading to a universal behavior. This limit is marked by equal probabilities for forward and backward scattering. Notwithstanding this non-trivial scattering pattern, we find that the shot noise as well as zero cross-current correlations vanish. We thus present a paradigmatic picture of an impurity in the Luttinger model, alternative to the Kane-Fisher picture.

Field-theoretical approach to Anderson localization in 2D disordered fermionic systems of chiral symmetry classes (BDI, AIII, CII) is developed. Important representatives of these symmetry classes are random hopping models on bipartite lattices at the band center. As was found by Gade and Wegner two decades ago within the sigma-model formalism, quantum interference effects in these classes are absent to all orders of perturbation theory. We demonstrate that the quantum localization effects emerge when the theory is treated non-perturbatively. Specifically, they are controlled by topological vortex-like excitations of the sigma models. We derive renormalization group equations including these non-perturbative contributions. Analyzing them, we find that the 2D disordered systems of chiral classes undergo a metal-insulator transition driven by topologically induced Anderson localization. We also show that the Wess-Zumino and Z_2 theta terms on surfaces of 3D topological insulators (in classes AIII and CII, respectively) overpower the vortex-induced localization.

po rabote E.J. König, P. M. Ostrovsky, I. V. Protopopov, A. D. Mirlin, "Metal-insulator transition in 2D random fermion systems of chiral symmetry classes", arXiv:1201.6288v1

Budet sdelan kratkii (minut na 30) kommentarii na temu, obsuzhdavshuyusya G. Lesovikom na ego doklade 15 dekabrya v IFP, s ispol'zovaniem resheniya (E. Cuevas, M. Feigel'man, L.Ioffe, M. Mezard) zadachi o reshetke spinov so sluchainym polem, rasskazannoi ranee (21.10.2011).

Budet predstavleno bolee podrobnoe izlozhenie rezul'tatov raboty E.Cuevas, M.Feigelman, L.Ioffe, M.Mezard "Level statistics of disordered spin-1/2 systems and its implications for materials with localized Cooper pairs", ob'yavlennykh v sentyabre na Uchenom Sovete ITF.

Obsuzhdaetsya obobshchenie fluktuatsionnogo deistviya Ginzburga-Landau v sigma-modeli Keldysha na sluchai proizvol'nykh temperatur i magnitnykh polei . Etot podkhod pozvolyaet vosproizvesti standartnye rezul'taty dlya fluktuatsionnykh popravok vo vsei oblasti vyshe perekhoda, a takzhe poluchit' novye rezul'taty dlya effekta Kholla, voznikayushchego za schet sverkhprovodyashchikh fluktuatsii.

Obzornyi doklad po rabotam o Spin Seebeck Effect (otklik spinovogo toka na gradient temperatury):
Theory of magnon-driven spin Seebeck effect, arxiv:1009.0318
Gigantic enhancement of spin Seebeck effect by phonon drag, arxiv:1010.4600
Acoustic spin pumping as the origin of the long-range spin Seebeck effect, arxiv:1103.6120

Izucheny admittans i dissipatsiya energii v odno-elektronnoi korobke (malen'kii metallicheskii ostrovok, soedinennyi s rezervuarom tunnel'nym kontaktom; potentsial elektronov na ostrovke kontroliruetsya dopolnitel'nym zatvornym elektrodom) v neravnovesnom rezhime pri prilozhenii peremennogo zatvornogo napryazheniya v rezhime sil'noi kulonovskoi blokady. Vychislen admittans pri ne slishkom nizkoi effektivnoi temperature (energii) elektronov na ostrovke, kogda mozhno prenebrech' elektronnoi kogerentnost'yu, no neobkhodimo polnost'yu uchityvat' kvantovye fluktuatsii zaryada iz-za sil'nogo kulonovskogo vzaimodeistviya. Kak okazalos', dissipatsiya energii mozhet byt' vyrazhena cherez soprotivlenie zaryadovoi relaksatsii i perenormirovannuyu zaryadovuyu emkost' dazhe v neravnovesnykh usloviyakh. Povedenie admittansa kak funktsii vneshnei chastoty opredelyaetsya funktsiei raspredeleniya, otvechayushchei bozonnym kollektivnym vozbuzhdeniyam na ostrovke. Poetomu, mozhno ispol'zovat' admittans odno-elektronnoi korobki dlya izmereniya etoi bozonnoi funktsii raspredeleniya.

Vychislen tok v rezhime ko-tunnelirovaniya cherez dvukhurovnevuyu kvantovuyu tochku slabo svyazannuyu s ferromagnitnymi kontaktami. Pokazano, chto zavisimost' differentsial'nogo kondaktansa ot prilozhennogo napryazheniya imeet vid stupenek, kotorye razlichny v sluchayakh parallel'noi i antiparallel'noi orientatsii magnitnykh momentov v kontaktakh. Vklady v tok ot uprugikh i neuprugikh protsessov rassmotreny otdel'no. Naideno, chto v neuprugoi chasti toka ko-tunnelirovaniya est' interferentsionnaya chast' (zavisimost' ot faz tunnel'nykh amplitud).

Izuchaetsya perekhod ot dvukhchastichnoi zadachi Kupera k mnogochastichnoi modeli Bardina-Kupera-Shriffera (BKSh). Dlya opisaniya osnovnogo sostoyaniya sistemy predlozhen analiticheskii sposob resheniya uravnenii Richardsona, matematicheski ogranichennyi razrezhennym predelom kuperovskikh par. Nesmotrya na eto ogranichenie, sopostavlenie s rezul'tatami teorii BKSh ukazyvaet na to, chto poluchennye rezul'taty ostayutsya tochnymi i v plotnom rezhime par. Predlagaetsya al'ternativnaya interpretatsiya rezul'tatov teorii BKSh dlya energii osnovnogo sostoyaniya v terminakh "energii svyazi kuperovskoi pary", evolyutsioniruyushchei prostym obrazom pri perekhode ot razrezhennogo k plotnomu rezhimu par. V etom podkhode shchel' tipa BKSh v spektre vozbuzhdenii yavlyaetsya pryamym sledstviem mnogochastichnykh effektov, vyzvannykh blokirovkoi otdel'nykh odnoelektronnykh sostoyanii.

Temperaturnaya zavisimost' provodimosti na perekhode mezhdu plato v rezhime tselochislennogo kvantovogo effekta Kholla opredelyaetsya kriticheskim indeksom κ, kotoryi est' otnoshenie indeksa korrelyatsionnoi dliny (ν) i indeksa dliny razfazirovki (p), κ=p/(2ν). V otlichie ot indeksa korrelyatsionnoi dliny, kotoryi mnogo raz vychislyalsya, indeks p izuchalsya tol'ko v rabotakh [1,2]. V etikh rabotakh indeks p dliny razfazirovki byl vychislen v predpolozhenii, chto on opredelyaetsya anomal'noi razmernost'yu irrelevantnogo operatora, vkhodyashchego v `inverse participation ratio'. V rabote my analiticheski pokazyvaem, chto dlya sluchaya ekranirovannogo kulonovskogo vzaimodeistviya v singletnom kanale eto predpolozhenie vypolnyaetsya dlya Andersonovskogo perekhoda v unitarnom klasse v razmernosti 2+ε. Provedennye chislennye raschety ukazyvayut na to, chto eto predpolozhenie vypolnyaetsya i dlya perekhoda mezhdu plato.

My issleduem relaksatsionnuyu dinamiku elektronov v odnoelektronnom tranzistore. Imenno, my otvechaem na sleduyushchii vopros. Predpolozhim, chto neravnovesnoe elektronnoe raspredelenie obrazovalos' v protsesse eksperimenta. Po kakomu zakonu ono budet relaksirovat' k ravnovesiyu? Issledovanie relaksatsii provedeno v rezhimakh slaboi i sil'noi kulonovskoi blokady. Vyvedeny i resheny osnovnye kvantovye kineticheskie uravneniya, upravlyayushchie dinamikoi funktsii raspredeleniya v protsesse ustanovleniya teplovogo ravnovesiya. Ustanovleny universal'nye formuly dlya transportnykh koeffitsientov, prigodnye dlya tranzistora s tunnel'noi svyaz'yu lyuboi prozrachnosti. Krome togo, osushchestvlena odnopetlevaya perenormirovka osnovnykh fizicheskikh velichin, opredelyayushchikh transportnye nablyudaemye, chto pozvolyaet nam poluchit' naibolee tochnye rezul'taty.

Budet predstavleny predvaritel'nye rezul'taty chislennogo issledovaniya spektra i korrelyatsionnykh funktsii v spetsial'noi modeli 2-mernoi Boze-zhidkosti (s nerelyativistskoi supersimmetriei), dopuskayushchei modelirovanie kvantovykh svoistv pri pomoshchi klassicheskoi molekulyarnoi dinamiki.

Dlya sistem s sil'nymi korrelyatsiyami, pri otsutstvii yavnogo malogo parametra, prakticheski edinstvennym effektivnym metodom opisaniya yavlyayutsya interpolirushchie teorii, osnovannye na priblizheniyakh effektivnoi sredy. V chastnosti, dlya opisaniya sistem sil'nokorrelirovannykh elektronov rasprostranenie poluchil dinamicheskii metod srednego polya (DMFT), polnost'yu opisyvayushchii fiziku lokal'nykh (na uzle reshetki) elektronnykh fluktuatsii, no prenebregayushchii prostranstvennoi dispersiei korrelyatsii. Predlagaemyi metod, startuya s rezul'tata DMFT, pozvolyaet uchest' effekty prostranstvennoi dispersii posredstvom regulyarnogo diagrammnogo razlozheniya. Metod osnovan na tochnom perekhode k ansamblyu dual'nykh peremennykh, gaussovo priblizhenie dlya kotorogo vosproizvodit DMFT, a diagrammnoe razlozhenie po nelineinosti pozvolyaet utochnit' etot rezul'tat. Dlya poluzapolnennoi modeli Khabbarda na kvadratnoi reshetke uchet prosteishei diagrammnoi popravki v rezhime sil'nykh korrelyatsii (U=8..16 t) pozvolyaet izbavit'sya ot nefizichnogo tsentral'nogo pika plotnosti odnoelektronnykh sostoyanii, a summirovanie lestnichnogo ryada - poluchit' antiferromagnitnuyu psevdoshchel'. Dlya modeli s dopirovaniem, opisano anizotropnoe razrushenie poverkhnosti Fermi v rezhime psevdoshcheli i effekty perenormirovki zakona dispersii vblizi osobennostei van Khova.

Doklad posvyashchen neravnovesnoi kinetike dvumernogo elektronnogo gaza na vysokikh urovnyakh Landau v usloviyakh mikrovolnovogo oblucheniya i/ili sil'nogo (v tom chisle neodnorodnogo) elektricheskogo polya. Budet predstavlena teoriya (osnovannaya na reshenii kvantovogo kineticheskogo uravneniya v prisutstvii plavnogo i korotkodeistvuyushchego potentsiala primesei, a takzhe elektron-elektronnogo i elektron-fononnogo vzaimodeistviya), pozvolyayushchaya v ramkakh edinogo podkhoda opisat' razlichnye tipy ravnovesnykh i neravnovesnykh magnetoostsillyatsii, nablyudaemykh v eksperimente. Pomimo Shubnikovskikh ostsillyatsii, syuda otnosyatsya ostsillyatsii magnetosoprotivleniya, indutsirovannye sil'nym postoyannym tokom, mikrovolnovym oblucheniem, i rezonansnym vzaimodeistviem s teplovymi fononami, a takzhe kvantovye ostsillyatsii koeffitsienta pogloshcheniya mikrovoln i szhimaemosti elektronnogo gaza. Takzhe budet predstavlena teoriya fotogal'vanicheskikh yavlenii v neodnorodnom elektronnom gaze. Budet pokazano, chto fotoeds v takikh neravnovesnykh sistemakh voznikaet vsledstvie narusheniya sootnosheniya Enshteina mezhdu provodimost'yu i koeffitsientom diffuzii.

Vychislyaetsya popravka k provodimosti Sharvina dvumernogo ballisticheskogo mikrokontakta s bol'shim chislom kvantovykh kanalov. Ona voznikaet iz-za elektron-elektronnogo vzaimodeistviya, i mozhet byt' poluchena uzhe v kvaziklassicheskom predele. Popravka polozhitel'na, vozrastaet s temperaturoi i rezko umen'shaetsya s rostom magnitnogo polya. Poluchennye rezul'taty kachestvenno i kolichestvenno ob'yasnyayut anomal'noe polozhitel'noe magnetosoprotivlenie v malykh polyakh, nedavno nablyudavsheesya na eksperimente.

We report thermodynamic magnetization measurements of a 2-dimensional electron gas for several high mobility Si-MOSFETs. The low-temperature magnetization is shown to be strongly sub-linear function of the magnetic field. The susceptibility determined from the zero-field slope grows with cooling as 1/T^α, with α=2.4±0.2 even at high electron densities, in apparent contradiction with the Fermi-liquid picture.

izlozhenie rezul'tatov preprintov:
arxiv: 0904.0690 Topological insulators in three dimensions from spontaneous symmetry breaking, Yi Zhang, Ying Ran, Ashvin Vishwanath
arxiv: 0907.2962 Mott physics and band topology in materials with strong spin-orbit interaction, D. A. Pesin, and Leon Balents

Izuchaetsya kulonovskaya blokada v odno-elektronnom tranzistore v neravnovesnom rezhime (naprimer, kogda temperatura ostrovka bol'she temperatury rezervuarov). V sluchae tunnel'nykh kontaktov mezhdu ostrovkom i rezervuarami polucheno kvantovoe kineticheskie uravnenie na funktsiyu raspredeleniya elektronov na ostrovke. S pomoshch'yu nego reshena zadacha o relaksatsii temperatury ostrovka za schet mekhanizma tunnelirovaniya elektronov s ostrovka v rezervuary i obratno.

V rabote izuchaetsya zaryad v kvantovoi tochke, prisoedinennoi k sverkhprovodyashchim beregam pri nalichii kulonovskogo i elektron-fononnogo vzaimodeistvii v predele beskonechnoi sverkhprovodyashchei shcheli. Rassmotreno vliyanie fononov na chuvstvitel'nost' zaryada k raznitse sverkhprovodyashchikh faz. Pokazano, chto, v nekotorom smysle, elektron-fononnoe vzaimodeistvie deistvuet kak "otritsatel'noe" kulonovskoe vzaimodeistvie.

I will review old and recent results for eigenfunction and eigenvalue statisitics of certain random matrix ensembles and show the correspondence between them and statistics in the 3D Anderson model at criticality. From the conventional viewpoint of RMT the two ensembles belong to distinctly different universality classes, being invariant and non-invariant with respect to rotation of basis, respectively.

Yet we show the similarity of their level statistics and a possibility of unifying them using the Luttinger liquid formalism. We also show that the level correlations in the invariant RMT show properties similar to expected density correlations in the sonic analogue of black holes.

Planiruetsya rasskazat' o topologicheskikh izolyatorakh s T-simmetriei so "standartnoi" tochki zreniya (polyarizatsiya otnositel'no obrashcheniya vremeni pervichna, poverkhnostnye urovni vtorichny) po stat'yam Fu i Kane "Time reversal polarization and adiabatic spin pump" (2006) i "Topological insulators with inversion symmetry" (2007). Esli poluchitsya, to mozhno budet zadet' i obshchuyu klassifikatsiyu po Kitaevu.

v kotoroi izuchaetsya RKKY vzaimodeistvie na poverkhnosti topologicheskogo izolyatora, a takzhe o ryade rabot svyazannykh s etim voprosom.

V programme zasedaniya:
11.30-12.15 G.E. Volovik «Sila Iordanskogo i kvantovaya turbulentnost'»
12.15-13.00 A.M. Finkel'shtein «Effektivnaya teoriya rasprostraneniya impul'sov v nelineinykh i neuporyadochennykh sredakh»
13.00-13.15 Pereryv
13.15-14.00 S.E. Korshunov «Fazovye perekhody v dvumernykh reshetkakh SFS kontaktov»
14.00-14.45 E.A. Brener «Asimptoticheskie nelineinosti v smektikakh»
15.00-17.00 Furshet

Spin and Charge Correlations in Quantum Dots: An Exact Solution (for the Tunneling Density of States)

I.Burmistrov, Y. Gefen, M. Kiselev

Abstract: The inclusion of charging and spin-exchange interactions within the Universal Hamiltonian description of quantum dots is challenging as it leads to a non-Abelian action. Here we present an exact analytical solution of the probem, in particular, in the vicinity of the Stoner instabilty point. We specifically calculate the tunneling density of states (TDOS) and the spin susceptibility. Near the instability point the TDOS exhibits a non-monotonous behavior as function of the tunneling energy, even at temperatures higher than the exchange energy. Our approach is generalizable to a broad set of observables, including the a.c. susceptibility and the absorption spectrum for anisotrpic spin interaction. Our results could be tested in nearly ferromagnetic materials.

Eksperimental'no obnaruzheny znakoperemennye ostsillyatsii fototoka i foto-EDS, voznikayushchie pri mikrovolnovom obluchenii neodnorodnykh obraztsov s dvumernymi elektronnymi sistemami. Polozhenie ostsillyatsii sootvetstvuet polozheniyu garmonik tsiklotronnogo rezonansa. Pokazano, chto vozniknovenie fotosignalov svyazano so vstroennym v obraztse elektricheskim polem. V etom sluchae ostsillyatsii fototoka sootvetstvuyut ego protekaniyu vdol' i protiv elektricheskogo polya, a ostsillyatsii foto-EDS otrazhayut libo ekranirovanie, libo usilenie elektricheskogo polya foto-vozbuzhdennymi elektronami.

V teoreticheskoi chasti raboty pokazano, chto vozniknovenie foto-gal'vanicheskikh signalov svyazano s narusheniem v neravnovesnom sostoyanii sootnosheniya Einshteina mezhdu provodimost'yu i koeffitsientom diffuzii. Vychislennye provodimost' i koeffitsient diffuzii dvumernoi elektronnoi sistemy pod oblucheniem, a takzhe vol't-ampernaya kharakteristika obraztsa s omicheskimi kontaktami pozvolyayut ob'yasnit' eksperimental'nye nablyudeniya.

[1] S.I. Dorozhkin, I.V. Pechenezhskii, L.N. Pfeiffer, K.W. West, V. Umansky, K. von Klitzing, J.H. Smet, Photocurrent and photovoltage oscillations in the two-dimensional electron system: enhancement and suppression of built-in electric fields, Phys. Rev. Lett. 102, 036602 (2009).

[2] I.A. Dmitriev, S.I. Dorozhkin, and A.D. Mirlin, Theory of the microwave-induced photocurrent and photovoltage magneto-oscillations in a spatially non-uniform 2D electron gas.

Quantum mechanics offers novel algorithms speeding up the solution of specific computational tasks. While applications in quantum cryptography are close to commercial realization, building a universal quantum computer with thousands of quantum bits lies in the distant future, if ever realized. In this situation, it is interesting to consider special tasks, less demanding in their requirements regarding the number of qubits and the network complexity. Here, we discuss an algorithm and its application where a few qubits serve as active or passive detectors. The core algorithmic element is a setup with K qubits allowing to count the elements in a stream of particles flowing in a quantum wire and represent it in a binary form. Applications include a divisibility-check to experimentally determine the size of a finite train of particles in a quantum wire and a scheme allowing to entangle multi-particle wave functions in a Mach-Zehnder interferometer, generating Bell-, Greenberger-Horne-Zeilinger-, or Dicke states.

referativnyi doklad po eksperimental'noi rabote V.Deshpandei, D.Novikov, M.Bockgrath et al, Science, v.323, p.106 (2009)

referativnyi doklad po rabote L. Glazman, A. Imambekov, arXiv:0812.1046

Issleduetsya zadacha o dissipatsii energii v zadache o metallicheskom ostrovke, soedinennym tunnel'nym kontaktom s rezervuarom, i emkost'yu s zatvorom, na kotoroe podaetsya peremennoe napryazhenie. Formuly dlya dissipatsii energii s uchetom kulonovskoi energii na ostrovke polucheny v dvukh predel'nykh sluchayakh: malykh i bol'shikh kondaktansov tunnel'nogo kontakta. Poluchennye rezul'taty pozvolyayut sdelat' predpolozhenie ob universal'nosti poluchennykh formul pri lyubykh kondaktansakh tunnel'nogo perekhoda.

po rabote:

arXiV:0802.0379 Creation and manipulation of anyons in the Kitaev model S. Dusuel, K. P. Schmidt, J. Vidal

We analyze the effect of local spin operators in the Kitaev model on the honeycomb lattice. We show, in perturbation around the isolated-dimer limit, that they create Abelian anyons together with fermionic excitations which are likely to play a role in experiments. We derive the explicit form of the operators creating and moving Abelian anyons without creating fermions and show that it involves multi-spin operations. Finally, the important experimental constraints stemming from our results are discussed.

Violation of Kirchhoff's Laws for a Coherent RC Circuit, J.Gabelli, et al, Science 313, 499 (2006)

i obzor lezhashchei v ee osnove teoreticheskoi raboty:

Buttiker, Thomas, Pretre, Phys. Lett. A 180, 364 (1993)

(doklad o zadache, nakhodyashcheisya v rabote)

Budet rasskazano o poluchennykh k nastoyashchemu vremeni analiticheskikh rezul'tatakh dlya SINIS perekhoda v rezhime zadannogo napryazheniya: vychislenie zavisyashchego ot vremeni toka v dissipativnom rezhime.

1) M. Dolev, M. Heiblum, V. Umansky, A. Stern, D. Mahalu, "Observation of a quarter of an electron charge at the \nu=5/2 quantum Hall state", Nature 452, 829 (2008) [arXiV:0802.0930]

2) 2) I.P. Radu, J.B. Miller, C.M. Marcus, M.A. Kastner, L.N. Pfeiffer, K.W. West, "Quasi-particle properties from tunneling in the \nu=5/2 fractional quantum Hall state", Science 320, 899 (2008) [arXiV:0803.3530]

Bergeret, Volkov, Efetov, "Induced ferromagnetism due to superconductivity in superconductor- ferromagnet structures", PRB 69, 174504 (2004); "Spin screening of magnetic moments in superconductors", Europhys. Lett. 66, 111 (2004).

Rassmotren kondaktans kvantovoi tochki s kulonovskim vzaimodeistviem v situatsii, kogda na tochku posylaetsya konechnoe chislo odnoelektronnykh volnovykh paketov. Iskhodya iz znaniya tochnoi N chastichnoi matritsy rasseyaniya sistemy pokazano, chto v sluchae nesimmetrichnoi kvantovoi tochki (otnositel'no zameny levo/pravo) pri nalichii vzaimodeistviya kondaktans sistemy okazyvaetsya takzhe asimmetrichnym otnositel'no napravleniya perenosa zaryada.

V rabote issleduetsya vliyanie spinovogo i dolinnogo rasshcheplenii na soprotivlenie, spinovuyu i dolinnuyu vospriimchivost' dvumernoi neuporyadochennoi elektronnoi zhidkosti. Kak vyyasnilos', v rabote na etu zhe temu, rasskazannoi god nazad, nami byla dopushchena oshibka. V doklade budet rasskazano o novykh odnopetlevykh uravneniyakh renorm-gruppy, kotorye opisyvayut sistemu v dvukh oblastyakh Δ_s << T << Δ_v i T << Δ_s << Δ_v, gde T - temperatura, Δ_s -spinovoe rasshcheplenie, i Δ_v - dolinnoe rasshcheplenie. S pomoshch'yu poluchennykh uravnenii renorm-gruppy nam udalos' kachestvenno ob'yasnit' proiskhozhdenie nemonotonnoi zavisimosti soprotivleniya ot temperatury, kotoraya nablyudaetsya eksperimental'no v parallel'nom magnitnom pole, a takzhe predskazat' vozmozhnost' nablyudeniya novogo tipa nemonotonnogo povedeniya, pri kotorom soprotivlenie kak funktsiya temperatury imeet dva maksimuma.

V priblizhenii tunnel'nogo gamil'toniana rassmatrivaetsya model' kvantovoi tochki, pomeshchennoi mezhdu dvumya sverkhprovodyashchimi provodnikami, k kotorym prilozhena raznost' potentsialov. Dopolnitel'no ryadom s tochkoi pomeshchen normal'nyi provodnik, po kotoromu ne techet tok: on igraet rol' rezervuara, sbivayushchego fazu tunneliruyushchikh v nego elektronov. Pri pomoshchi neravnovesnoi Keldyshevskoi tekhniki vychislyaetsya podshchelevoi elektricheskii tok, kotoryi, kak izvestno, voznikaet v protsesse perenosa zaryada pri mnozhestvennykh Andreevskikh otrazheniyakh. Pokazano, chto svyaz' s normal'nym provodnikom privodit k sglazhivaniyu osobennostei v postoyannom toke, voznikayushchikh pri mnozhestvennykh Andreevskikh otrazheniyakh. S drugoi storony, pervaya garmonika toka na Dzhozefsonovskoi chastote bolee ustoichiva k sboyu fazy, dazhe dlya napryazhenii, men'shikh sverkhprovodyashchei shcheli. Faza etoi pervoi garmoniki pozvolyaet provodit' izuchenie effektov, vyzvannykh normal'nym provodnikom.

Na primere billiarda Sinaya izucheno vliyanie difraktsii na spektral'nye kharakteristiki khaoticheskikh billiardov, granitsa kotorykh imeet vognutye vovnutr' uchastki. Difraktsiya privodit k poyavleniyu tselogo mnozhestva dopolnitel'nykh traektorii pomimo klassicheskikh. Vychislen "nediagonal'nyi" vklad ot nikh v korrelyatsionnuyu funktsiyu dvukh urovnei energii, proiskhodyashchii ot interferentsii mezhdu nimi. Pokazano, chto on yavlyaetsya ostsilirruyushchei funktsiei chastoty s periodom, ravnym t.n. vremeni Erenfesta.

Issleduyutsya instantonnye popravki k soprotivleniyu v neodnorodnom granulirovannom metalle. Obsuzhdaetsya kachestvennaya fizicheskaya kartina fiziki sistemy v sluchae prosteishei neodnorodnosti.

Zaryad podshchelevogo sostoyaniya v andreevskoi kvantovoi tochke (AKT), pomeshchennoi v sverkhprovodyashchuyu petlyu, ochen' chuvstvitelen k magnitnomu potoku, pronikayushchemu v petlyu. My obsuzhdaem vozmozhnost' ispol'zovaniya etoi ustanovki kak pribora dlya izmereniya slabykh magnitnykh potokov. My detal'no izuchili chuvstvitel'nost' kak funktsiyu parametrov AKT v predele Δ → ∞. Takzhe my izuchili slaboe kulonovskoe vzaimodeistvie v AKT.

My predlagaem novuyu model'nuyu sistemu dlya izucheniya perekhoda sverkhprovodnik-izolyator. Eta sitema predstavlyaet soboi regulyarnuyu reshetku, kazhdoe rebro kotoroi sostoit iz N>>1 dzhozefsonovskikh kontaktov, soedinennykh posledovatel'no. Dlya sluchaya, kogda dzhozefsonovskaya energiya kontaktov velika po sravneniyu s zaryadovoi, razvita teoriya, opisyvayushchaya takuyu setku. Vyvedeno tochnoe dual'noe preobrazovanie, perevodyashchee gamil'tonian iskhodnoi sistemy v standartnyi gamil'tonian dzhozefsonovskoi setki na kvadratnoi reshetke. Dlya magnitnykh frustratsii f=0, 1/2, 1/4 naideno kriticheskoe otnoshenie E_J/E_C, pri kotorom v rassmatrivaemoi sisteme proiskhodit nul'temperaturnyi perekhod sverkhprovodnik-izolyator, i opredelena zavisimot' temperatury sverkhprovodyashchego perekhoda ot E_J/E_C. Analogichnye velichiny otseneny dlya sluchaya nulevoi magnitnoi frustratsii, no v prisutstvii sil'noi sluchainoi zaryadovoi frustratsii.

V rabote rassmatrivaetsya vopros ob izmerimosti fluktuatsii toka vysshikh poryadkov lineinym detektorom. Rassmotreny dva razlichnykh tipa izmerenii: izmerenie spektral'noi moshchnosti fluktuatsii i izmerenie raznovremennykh korrelyatorov toka pri fiksirovannykh vremenakh. Dlya kazhdogo sluchaya polucheny formal'no tochnye vyrazheniya dlya pokazanii detektora, soderzhashchie uporyadochennye vdol' Keldyshevskogo kontura operatory elektronnogo toka. Naiden yavnyi vid vremennogo uporyadocheniya operatorov toka pod znakom srednego pri izmerenii raznovremennykh korrelyatorov toka vysshikh poryadkov. Rassmotrena situatsiya, kogda detektor izmeryaet korrelyatsii toka v razlichnykh tochkakh provodnika.

My rassmotrim zadachu o rasseyanii ploskoi volny na prepyatstvii ili neodnorodnostyakh. Transportnoe sechenie rasseyaniya sigma_T malo izucheno dazhe dlya potentsialov obladayushchikh tsentral'noi simmetriei. V sluchae zhe prepyatstviya proizvol'noi formy amplituda rasseyaniya prakticheski ne poddaetsya informativnomu analiticheskomu opisaniyu. Tem ne menee, v nekotorykh sluchayakh nam udalos' poluchit' nekotoruyu informatsiyu, vychislyaya i sravnivaya polnoe i transportnoe secheniya rasseyaniya, a takzhe reshaya zadachu o minimizatsii (maksimizatsii) sigma_T.

Pri nizkoi plotnosti, elektrony v kvantovoi provoloke mogut obrazovat' vignerovskii kristall. V etom sluchae geizenbergovskii obmen mezhdu paroi blizhaishikh elektronov voznikaet v rezul'tate tunnelirovaniya pod razdelyayushchim ikh kulonovskim bar'erom. Pri etom kulonovskoe vzaimodeistvie vovlekaet v protsess tunnelirovaniya i vse ostal'nye elektrony, ch'e vliyanie na velichinu konstanty geizenbergovskogo obmena my i izuchaem - kak analiticheski, tak i chislenno.

po rabote R.S. Keizer, M.G. Flokstra, J. Aarts i T. M. Klapwijk