# Colloquium

## TBA

24 мая в 11:30

C. Glattli (France)

## TBA

26 апреля в 11:30

Boris Narozhny (KIT)

## On reconstructing nonlinearly encrypted signals corrupted by noise.

12 апреля в 11:30

Ян Федоров

I consider the problem of reconstructing a source vector from its encrypted image corrupted by an additive Gaussian noise.
Assuming encryption to be given by a random Gaussian mapping, the reconstruction problem in the framework of the Least Square Scheme
turns out to be equivalent to finding the configuration of minimal energy in a certain version of spherical spin glass model.
As a measure of the quality of the signal reconstruction one can use the mean overlap between the original signal and its recovered image.
Thi overlap is analysed in the framework of Parisi scheme of Replica Symmetry Breaking. If the mapping is quadratic,
there exists a threshold in the noise-to-signal ratio beyond which
the reconstruction is impossible. The behaviour close to the threshold is controlled by the replica symmetry breaking mechanism and
is characterized by a nontrivial exponent 3/4.

## Correlation-induced localization

5 апреля в 11:30

Владимир Кравцов

Conventional Anderson localization is due to destructive interference of
matter waves described by local random Hamiltonians. Correlations in
random diagonal elements of such a Hamiltonian are known to favor
delocalization. Recently systems with non-local Hamiltonians become
experimentally accessible. We consider two families of such random
matrix Hamiltonians with correlations in the long-range hopping terms
and demonstrate that localization is enhanced and the wave function
ergodicity is progressively degrading as the correlations become stronger.
We review the localization/delocalization criteria of Mott and Anderson
and show that the former is the sufficient criterion of weak ergodicity
and the latter is the sufficient criterion of localization. The fact
that these two criteria are not complimentary is the reason why the
non-ergodic extended (multifractal) states may exist when neither the
Mott, nor the Anderson criterion is fulfilled.

We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.

Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.

We suggest a new class of random matrix models (Toeplitz RMT) with translation-invariant hopping integrals and identify the character of eigenfunction and eigenvalue statistics in them. We formulate the principles of level statistics if the type of eigenfunction statistics is known both in the coordinate and in the momentum basis and demonstrate that for the Toeplitz RMT the ergodic delocalization in the coordinate space may coexist with the Poisson level statistics.

Finally, we suggest a matrix-inversion trick that allows to identify uniquely the type of eigenfunction statistics and prove the absence of delocalized states in the bulk of spectrum of long-range Hamiltonians with deterministic (fully correlated) hopping.

## Recent theoretical developments in the integer quantum Hall effects

22 февраля в 11:30

Ferdinand Evers (Regensburg University)

The quantum Hall effects belong to the most striking phenomena in condensed matter physics. Despite of intensive theoretical efforts over the last three decades, important aspects of the quantum Hall transitions are still not fully understood. In particular, there is still no consensus concerning the critical field theory and the corresponding scaling properties of the observables near and at the plateau transition.

Notwithstanding this status, the last ten years have seen considerable progress in understanding basic properties of scaling near localization-delocalization transitions that have implications also for the quantum Hall transition. These concern, e.g., the important topic of corrections to scaling, the wavefunction statistics and higher-order multifractality. A brief review of these developments will be offered in the first part of the talk.

The second part of the talk will be devoted to the spin quantum Hall effect, which is a variant of the integer quantum Hall effect (class A) taking place in the Altland-Zirnbauer class C. For this transition several critical exponents are known analytically and can serve as reference points. Therefore, this transition provides an ideal testbed for the qualitative predictions made by analytical theories. Analytical predictions will be confronted with most recent numerical results.

Notwithstanding this status, the last ten years have seen considerable progress in understanding basic properties of scaling near localization-delocalization transitions that have implications also for the quantum Hall transition. These concern, e.g., the important topic of corrections to scaling, the wavefunction statistics and higher-order multifractality. A brief review of these developments will be offered in the first part of the talk.

The second part of the talk will be devoted to the spin quantum Hall effect, which is a variant of the integer quantum Hall effect (class A) taking place in the Altland-Zirnbauer class C. For this transition several critical exponents are known analytically and can serve as reference points. Therefore, this transition provides an ideal testbed for the qualitative predictions made by analytical theories. Analytical predictions will be confronted with most recent numerical results.

## Noisy quantum measurements: just a nuisance or fundamental physics?

7 декабря 2018 в 11:30

Wolfgang Belzig

Weak, almost non-invasive quantum measurements differ from the standard text book example of strongly invasive, projective measurements, since they leave the measured system basically unchanged. This opens the path to measure e.g. non-commuting observables and at the same time poses several open questions: Which order of operators is measured? Can quantum tests like Bell or Leggett-Garg be reformulated? What time scales are involved in the measurement process? We will address some basic properties of weak measurements leading to surprises like apparent spontaneous time-reversal symmetry breaking or the possibility of engineered detectors to tailor the measured quantum correlations.

## Эксперименты с ферми- и бозе-газами

30 ноября 2018 в 11:30

Андрей Турлапов, ИПФ РАН, г. Нижний Новгород

Способы достижения температур уровня нанокельвинов в атомных газах станут первой темой доклада. Далее будут приведены примеры интересных экспериментов с квантовыми газами. В то же время речь пойдёт о сложностях, которые встречаются в экспериментах и о возможных, ещё не реализованных, путях их преодоления. В заключении подробно будет обсуждаться неопубликованный эксперимент по интерференции цепочки бозе-конденсатов, в котором возникает пространственно периодическая интерференционная картина, несмотря на то, что относительные фазы конденсатов случайны.

Видео

Видео

## Гравитационно-волновая астрономия: в ожидании новых источников

9 ноября 2018 в 11:30

Константин Постнов (ГАИШ МГУ)

Будет проведен анализ первых лет работы гравитационно-волновых детекторов
LIGO/Virgo (сентябрь 2015 - август 2017), обнаруживших 6 слияний двойных черных дыр и одно слияние двойных нейтронных звезд. Будут рассмотрены основные результаты и возникшие проблемы в астрофизической интерпретации свойств источников. Новые наблюдения начнутся в феврале 2019 года.

## Wonders of viscous electronics

19 октября 2018 в 11:30

Gregory Falkovich (Weizmann Institute of Science, Israel)

Quantum-critical strongly correlated systems feature universal collision-dominated collective transport. Viscous electronics is an emerging field dealing with systems in which strongly interacting electrons flow like a fluid. Such flows have some remarkable properties never seen before. I shall describe recent theoretical and experimental works devoted, in particular, to a striking macroscopic DC transport behavior: viscous friction can drive electric current against an applied field, resulting in a negative resistance, recently measured experimentally in graphene. I shall also describe conductance exceeding the fundamental quantum-ballistic limit, field-theoretical anomalies and other wonders of viscous electronics. Strongly interacting electron-hole plasma in high-mobility graphene affords a unique link between quantum-critical electron transport and the wealth of fluid mechanics phenomena.

## Quantum electrodynamics of heavy ions and atoms

5 октября 2018 в 11:30

Владимир Моисеевич Шабаев (физфак СПбГУ)

The present status of the QED theory of heavy ions and atoms is reviewed. The theoretical predictions for the Lamb shifts, the hyperfine splittings, and the bound-electron g factors of highly charged few-electron ions are compared with available experimental data. Special attention is paid to tests of QED at strong-coupling regime and determination of fundamental constants. The current status of studying the parity nonconservation effects with heavy atoms is also reported. Recent results on the charge-transfer and pair-creation probabilities in low-energy heavy-ion collisions are presented. Prospects for tests of QED at supercritical fields are discussed.

## Superconductivity that breaks time-reversal symmetry and its experimental manifestations

28 сентября 2018 в 11:30

Victor Yakovenko (University of Maryland)

References:

- [1] X. Gong, M. Kargarian, A. Stern, D. Yue, H. Zhou, X. Jin, V. M. Galitski, V. M. Yakovenko, and J. Xia, Science Advances 3, e1602579 (2017), arXiv:1609.08538
- [2] P. M. R. Brydon, D. S. L. Abergel, D. F. Agterberg, and V. M. Yakovenko, arXiv:1802.02280

## Quantum Many-Body Physics of Qubits

22 июня 2018 в 11:30

Leonid Glazman (Yale University)

## Eukaryotic cell polarity and protein sorting

27 апреля 2018 в 11:30

Andrea Gamba, Politecnico di Torino

## Chiral magnetic crystals

23 марта 2018 в 11:30

Markus Garst (TU Dresden)

The weak Dzyaloshinskii-Moriya interaction in chiral cubic magnets like MnSi, FeGe or Cu2OSeO3 twists the magnetization on long length scales resulting in spatially periodic magnetic textures — magnetic crystals. There exist especially magnetic crystals with a one- and two-dimensional periodicity corresponding to the magnetic helix and the topologically non-trivial skyrmion lattice, respectively. In this talk, we provide an overview of their properties. In particular, we discuss the crystallization process of these magnetic crystals that is characterized by strongly correlated chiral paramagnons that drive the transition first-order [1,2]. This fluctuation-induced first-order transition is well described by a theory put forward by Brazovskii. We will introduce the magnon band structure and their non-reciprocal properties in the presence of a magnetic field [3,4]. For the skyrmion lattice, this band structure is topological and characterized by finite Chern numbers that can be attributed to the formation of magnon Landau levels due to an emergent orbital magnetic field [5,6,7]. Finally, we will discuss domain walls of helimagnets that share similarities with grain boundaries consisting of disclination and dislocation defects of the helimagnetic order [8].

Video

References:

- [1] M. Janoschek et al. Phys. Rev. B 87, 134407 (2013).
- [2] A. Bauer, M. Garst and C. Pfleiderer, Phys. Rev. Lett. 110, 177207 (2013).
- [3] M. Kugler et al. Phys. Rev. Lett. 115, 097203 (2015)
- [4] T. Weber et al. arXiv:1708.02098
- [5] C. Schütte and M. Garst, Phys. Rev. B 90, 094423 (2014).
- [6] T. Schwarze, J. Waizner, M. Garst, A. Bauer, I. Stasinopoulos, H. Berger, C. Pfleiderer, and D. Grundler, Nat. Mater. 14, 478 (2015).
- [7] M. Garst J. Waizner, and D. Grundler, J. Phys. D: Appl. Phys. 50, 293002 (2017)
- [8] P. Schoenherr et al. Nat. Phys. in press, arXiv:1704.06288

Video