8th Workshop on Quantum Chaos and Localisation Phenomena

19 - 21 May 2017 - Warsaw, Poland

Organisers
    * Institute of Physics, Polish Academy of Sciences
    * Center for Theoretical Physics, Polish Academy of Sciences
    * Pro Physica Foundation

Organising Committee
    * Szymon Bauch
    * Małgorzata Białous
    * Marek Kuś
    * Michał Ławniczak
    * Paweł Masiak
    * Leszek Sirko - Chairman
    * Vitalii Yunko

Workshop's Objectives

To assess achievements and to formulate directions of new research on quantum chaos and localisation. To bring together prominent experimental and theoretical physicists who share a common interest in quantum chaos and localisation phenomena.

Workshop's Scope

Presentations will focus on the following topics: Quantum chaos and nonlinear classical systems; Quantum and microwave billiards; Quantum and microwave graphs; Atoms in strong electromagnetic fields - experiment and theory; Chaos vs. coherent effects in multiple scattering; Anderson localisation; Random lasers; Quantum chaos and quantum computing; Entanglement and noise.

First Announcement

The 8th Workshop on Quantum Chaos and Localisation Phenomena will be held from May 19 to May 21, 2017 at the Institute of Physics of the Polish Academy of Sciences in Warszawa. Arrivals are planned on Friday, afternoon/evening (May 19). Departure will be on Sunday (May 21) evening or on Monday (May 22) morning if necessary. Please disseminate information about the Workshop among your students, collaborators and colleagues who might be interested.

Second Announcement

Deadlines:

Registration and Abstract Submission: April 18, 2017

Conference fee: 650 PLN (150 Euro)
The conference fee includes two lunches, conference dinner, and a social event on Saturday.
The fee for an accompanying person, which includes the conference dinner and the social event is: 220 PLN (50 Euro).
Limited number of grants for participants presenting posters will be available.

The payment should be transferred in Polish currency (złoty, PLN) or Euros to the bank account:

Bank Gospodarstwa Krajowego

Account number for PLN 89 1130 1017 0013 4373 9820 0025
Account number for Euros PL 35 1130 1017 0013 4373 9820 0027
SWIFT GOSKPLPW
Instytut Fizyki PAN, Warszawa
Chaos8

All bank charges are on the account of the payer. Please include in the bank transfer documents the names of the participants. The conference fee can be paid also by cash in Polish currency directly upon an arrival. However, such participants must register earlier.

Scientific programme:

-The workshop's programme will consist of invited talks and poster contributions.
-Invited talks are allotted either 35 minutes or 20 minutes (including approx. 5 minutes for questions/discussion).
-The lectures will start on Saturday, May 20, at 9 am.
-The poster session will be organized on Saturday. The posters will remain on display until Sunday, May 21. For poster presentation stands 155 cm high and 115 cm wide will be provided.


The invited talks will be published in Acta Physica Polonica A.
We kindly ask invited speakers to prepare their manuscripts according to the guide to authors.

Deadline for the manuscript submission: 16 August 2017.


Hotel information:

Sangate Hotel Airport**
ul. 17-go Stycznia 32, 02-148 Warszawa
tel. +48 (22) 576 45 50
email: rezerwacje@sangate.hotel.pl
(Hotel is located in the nearest vicinity of the airport.
Approximated price for workshop's participants (password: Chaos8): - a single room - 200 PLN, a double room - 240 PLN including breakfast)

Centrum Barnabitów*
(The Barnabite Centre)
ul. Smoluchowskiego 1, 02-679 Warszawa
tel. +48 (22) 543 20 01, 543 23 02
fax: +48 (22) 543 22 82
e-mail: info@barnabici.pl
(Prices: a single room - 178 PLN, a double room - 260 PLN, including breakfast)

Guest-house of the Institute of Physics PAS *
Al. Lotnikow 32/46, 02-668 Warszawa
phone: +48 (22) 843 24 24
e-mail: hotel@ifpan.edu.pl
(Prices: a single room - 135 PLN, a double room - 185 PLN, including breakfast)

* - walking distance to the Institute of Physics
** - transport to the Institute of Physics will be arranged by the organizers.

Invited Speakers

(Click on a name for more information)

* to be confirmed

Steven M. Anlage (College Park, USA)
E-Mail: anlage@umd.edu
WWW page: http://www.cnam.umd.edu/anlage/AnlageHome.htm
Affiliation: Physics Department, University of Maryland, College Park, MD 20742-4111, USA
Title: Nonlinear Wave Chaos
Abstract:
Many of the statistical properties of linear over-moded classical and quantum billiards have been successfully understood utilizing concepts from quantum/wave chaos. As an example, the Random Coupling Model (RCM) incorporates the universal fluctuations predicted by random matrix theory, and the system-specific features, to give a comprehensive description of wave scattering data on real-life linear wave chaotic systems [1 – 4]. We now wish to explore the wave chaotic properties of nonlinear systems. Our experiment involves a quasi-two-dimensional microwave billiard with a nonlinear active circuit attached at two ports of the otherwise linear system. The nonlinear circuit is designed to convert input signals at a given frequency f into output signals at frequency 2f (second harmonic generation). We inject waves into the billiard and measure the statistical properties of waves at both the linear and the second harmonic frequency. We find that the RCM can be extended to describe the statistical properties of second harmonic waves created by the nonlinear circuit in the billiard. We compare experimental results and extended RCM modeling and find good agreement. The prospects for further investigation of nonlinear wave chaotic systems will be discussed. This work was funded by ONR under Grant No. N000141512134, AFOSR under COE Grant FA9550-15-1-0171, COST Action IC1407 'ACCREDIT', supported by COST (European Cooperation in Science and Technology), and the Maryland Center for Nanophysics and Advanced Materials (CNAM).

Miguel Bastarrachea (Freiburg, Germany)
E-Mail: miguel.bastarrachea@physik.uni-freiburg.de
Affiliation: Institute of Physics Quantum Optics and Statistics Group, Albert Ludwig University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany
Title: Quantification of classical chaos in quantum atom-field systems
Abstract:
In this work we introduce a method to quantify chaos in quantum systems whose algebraic structure allows to obtain a classical phase space by means of coherent states. We employ the participation ratio (PR) of a coherent state spanned in the Hamiltonian eigenstate basis. We compare this quantity with the Lyapunov exponent over different energy regions and we show it allows for a detailed exploration of the semi-classical phase space employing only quantum tools. In order to test the method, we take advantage of the algebraic and critical properties of the Dicke Hamiltonian, a simple and paradigmatic model in quantum optics, which describes a set of two-level qubits interacting with a single mode of a bosonic field.

Edoardo Carnio (Coventry, UK)
E-Mail: e.carnio@warwick.ac.uk
Affiliation: Department of Physics, University of Warwick, PO Box: Gibbet Hill Road, Coventry CV4 7AL, UK
Title: The Anderson transition in doped silicon using 'ab initio' methods
Abstract:
The Anderson localization-delocalization transition (AT) has long been studied using paradigmatic models, but there is still no agreement on its critical exponent when comparing experiments and theory. In this work, we employ 'ab initio' methods to study the AT occurring in sulfur-doped silicon (Si:S) when increasing the dopant concentration. We use ONETEP, a linear-scaling implementation of DFT, to study model Si:S systems with few impurities, and we subsequently employ the resulting 'ab initio' Hamiltonians to build an effective tight-binding model for systems close to the critical concentration of the AT. We observe the formation of an impurity band, compute its density of state, and apply multifractal finite-size scaling of the wave functions to characterize the transition.

Barbara Dietz (Lanzhou University, Lanzhou, China)
E-Mail: dietz@ikp.tu-darmstadt.de
Affiliation: School of Physical Science and Technology, and Key Laboratory for Magnetism and Magnetic Materials of MOE, Lanzhou University, Lanzhou, Gansu 730000, China
Title: Chaos and regularity in the doubly magic nucleus 208^Pb
Abstract:
High resolution experiments have recently lead to a complete identification of the energy values, spin, and parity of 151 nuclear levels up to an excitation energy of Ex = 6.20 MeV in 208^Pb [1]. We present a thorough study of the fluctuation properties in the energy spectra. In a first approach we grouped states with the same spin and parity into subspectra, analyzed standard statistical measures for short- and long-range correlations in each sequence of unfolded energy levels and then computed their ensemble average. Their comparison with a random matrix ensemble which interpolates between Poisson statistics expected for regular systems and the Gaussian Orthogonal Ensemble (GOE) predicted for chaotic systems shows that the data are well described by the GOE. In a second approach, following an idea of Rosenzweig and Porter, we considered the complete spectrum composed of the spacings between adjacent unfolded energy levels of the independent subspectra. We analyzed their fluctuation properties using the method of Bayesian inference, which involves a chaoticity parameter f , which also interpolates between Poisson (f = 0) and GOE statistics (f = 1). It turns out to be f ≈ 0.9. This is so far the closest agreement with GOE observed in spectra of bound states in a nucleus. Thus, the spectral properties of the doubly magic nucleus 208^Pb coincide with those of a generic fully chaotic system. In the introduction we will present examples of classically chaotic systems which exhibit deviations from the expected GOE statistics, one example being quantum graphs where they may be attributed to non-universal contributions [3]. This work was published in [2]. It was supported by the Deutsche Forschungsgemeinschaft (DFG) within the Collaborative Research Centers CRC 634 and 1245.

Thomas Guhr (Duisburg-Essen, Germany)
E-Mail: thomas.guhr@uni-due.de
Affiliation: Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany
Title: Quantum Chaos in Many-Body Systems: Role of Collectivity
Abstract:
A wealth of information on chaotic systems has been accumulated during the last decades. In particular, the connection between chaotic classical dynamics and quantum chaotic levels statistics was ever better clarified, culminating in a heuristic understanding of the Bohigas-Giannoni-Schmit conjecture. The vast majority of these studies, however, focused on single-particle systems. In parts of the community it was almost forgotten that many-body systems were the motivation for Wigner's Random Matrix Theory which can be viewed as one of the important roots for the field of Quantum Chaos. Many-body systems pose new challenges: indistinguishability, the issue of spin-statistics as well as richer forms of motion which cannot occur in single-particle systems. Limits to some of the arguments in the context of the Bohigas-Giannoni-Schmit conjecture emerge. I will discuss our attempts to extend the concepts of Quantum Chaos, especially semiclassics, to many-body systems. In particular, we study collective motion in clouds of particles and in kicked spin chains. In the latter system, we show by consistent semiclassics how collectivity can fully dominate the dynamics. This drastically demonstrates the importance of genuine many-body effects for quantum chaos.

Ulrich Kuhl (Nice, France)
E-Mail: ulrich.kuhl@unice.fr
Affiliation: Laboratoire de Physique de la Matière Condensée (LPMC) CNRS UMR 7336 Université de Nice-Sophia Antipolis Parc Valrose 06108 Nice cedex 2, France
Title: Focusing inside Disordered Media with the Generalized Wigner-Smith Operator
Abstract:
We introduce a wavefront shaping protocol for focusing inside disordered media based on a generalization of the established Wigner-Smith time-delay operator. The key ingredient for our approach is the scattering (or transmission) matrix of the medium and its derivative with respect to the position of the target one aims to focus on. A specific experimental realization in the microwave regime is presented showing that the eigenstates of a corresponding operator are sorted by their focusing strength, ranging from strongly focusing on the designated target to completely bypassing it. Our protocol works without optimization or phase-conjugation and we expect it to be particularly attractive for optical imaging in disordered media.

Pavel Kurasov (Stockholm, Sweden)
E-Mail: kurasov@math.su.se
Affiliation: Institute of Mathematics, Stockholm University, SE-106 91, Stockholm, Sweden
Title: Surgery of graphs and spectral gap: Titchmarsh-Weyl operator-function approach
Abstract:
Titchmarsh-Weyl M-functions prove to be an effcient tool to study spectral and inverse problems for the one-dimensional Schrodinger equation. In my talk I shall prove an explicit formula for the M-function in the case of compact finite metric graphs. It will be applied to study behaviour of the spectrum under surgery of graphs which we understand as gluing of two graphs together by identifying few vertices or cutting a graph by chopping through some of its vertices. It appears that a precise answer can be given in terms of the corresponding Titchmarsh-Weyl (matrix) functions of the two subgraphs, more precisely in terms of their negative spectral subsaces. We illustrate our ndings by considering explicit examples. Partially this is a joint work with Sergey Naboko (Dept. of Mathematical Physics, Institute of Physics, St. Petersburg, State University).1

Jiri Lipovsky (Hradec Kralove, Czech Republic)
E-Mail: jiri.lipovsky@uhk.cz
Affiliation: Department of Physics, Faculty of Science, Rokitanskeho 62, 500 03 Hradec Kralove, Czech Republic
Title: The resonance asymptotics for point interactions in three dimensions
Abstract:
We assume finitely many point interactions in three dimensions. We introduce the resonance condition and the way how to obtain it. We study asymptotics of the number of resonances and find an example of such a distribution of interactions for which the leading term of the asymptotics is missing. We prove that the resonances for a non-trivial strength of the interaction converge to eigenvalues with strength equal to zero as their real part approaches to infinity.

Michał Ławniczak (Warsaw, Poland)
E-Mail: lawni@ifpan.edu.pl
Affiliation: Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Can one get information about the number of missing energy levels?
Abstract:
Analysis of energy spectra of quantum systems in the range where they are discrete sets can give us a lot of valuable information. Thanks to them we can, for example, determine chaotic character of the system and its class of symmetry in the RMT (Random Matrix Theory). Thus it is extremely important to know the number of missing energy levels in the real spectra of the studied systems. We present experimental studies of the power spectrum and other fluctuation properties in the spectra of microwave networks simulating chaotic quantum graphs with violated time reversal invariance and a three dimensional (3D) wave chaotic system represented by a 3D irregular microwave cavity. On the basis of the obtained data we demonstrate that the power spectrum together with other long-range and short-range correlations functions is a powerful tool for the determination of the fraction of missing levels and the identification of the studied system symmetry. This work was partially supported by the Ministry of Science and Higher Education, Grant No. UMO-2013/09/D/ST2/03727.

Klaus Richter (Regensburg, Germany)
E-Mail: Klaus.Richter@physik.uni-regensburg.de
Affiliation: Institut für Theoretische Physik, Universität Regensburg, 93040 Regensburg, Germany
Title: Many-body semiclassics for interacting bosons: Weyl law, trace formula and quantum phase transitions in the Lieb-Liniger model
Abstract:
A major objective of the semiclassical approach to interacting many-body systems is to combine the information of its two possible classical limits, namely a classical system of particles and a classical field theory, into an unified framework a la Gutzwiller, providing a picture of many-body interference based on coherent sums over classical solutions. Following this direction we will discuss recent progress in the semiclassical analysis of many-body quantum interference for a benchmark example of integrable quantum field theory, the Lieb-Liniger model, describing interacting bosons on a ring. We show that in the limit of high excitations its spectrum can be understood by means of suitable generalizations of the Weyl expansion for the smooth part, and a Berry-Tabor-like trace formula for the oscillatory part, revealing a spectral shell structure in terms of many-body periodic orbits. In the second part of the talk, we will show how the classical limit of the Lieb-Liniger model in the complementary limit of large particle number, given by a nonlinear Schroedinger equation, admits as well an analysis as an integrable classical system, now near its ground state. This enables the description of a sequence of quantum phase transitions arising for increasing attractive interaction, along with an understanding of numerical results for the spreading of information around criticality.

Alberto Rodríguez González (Freiburg, Germany)
E-Mail: Alberto.Rodriguez.Gonzalez@physik.uni-freiburg.de
Affiliation: Quantum Optics and Statistics, Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
Title: Exploiting multifractal fluctuations to characterise localisation-delocalisation transitions
Abstract:
At the critical point of the Anderson transition (AT) the single-particle eigenstates take an exotic form in which the various spatial iso-`surfaces' corresponding to different wavefunction intensities in the system are fractals. Most interestingly, the study of the flow of such multifractal fluctuations in the wavefunctions across the critical region provides an efficient numerical method to monitor and quantitatively characterise the transition. We demonstrate this for the 3-D AT in the unitary symmetry class, analysing more than 4 million independent wavefunctions of linear system sizes up to L=150. We also briefly mention the significance of multifractality in many-body systems and the possibility of applying this formalism to study localisation in Hilbert (Fock) space.

Dmitry Savin (London, UK)
E-Mail: Dmitry.Savin@brunel.ac.uk
WWW page: http://www.brunel.ac.uk/siscm/mathematical-sciences/people-in-maths/academic-staff/drdmitrysavin
Affiliation: Department of Mathematical Sciences, Brunel University, Uxbridge, UB8 3PH, UK
Title: Transmission via a simple mode on a chaotic background
Abstract:
Scattering on a resonant state coupled to a complicated background is a typical problem for mesoscopic quantum many-body systems as well as for wave propagation in the presence of a complex environment. On average, the coupling to background states leads to an effective damping of such a simple mode, expressed by the so-called ``spreading'' width. This talk will formulate and discuss an non-perturbative approach to study fluctuations in scattering, taking into account also finite dissipative losses in the background. Modelling the latter by random matrix theory, we employ the formalism of strength functions, adopted from nuclear physics, to derive exact expressions for the distribution functions of transmission and reflection. In particular, we discuss a sharp disappearance of the established transmission signal when the spreading width exceeds the natural width of the simple mode. Potential applications in the context of reverberation chambers and microwave communications are also briefly discussed.

Adam Sawicki (Warsaw, Poland)
E-Mail: assaw@cft.edu.pl
Affiliation: Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Asymptotic properties of entanglement polytopes for large number of qubits and RMT
Abstract:
Entanglement polytopes have been recently proposed as the way of witnessing the SLOCC multipartite entanglement classes using single particle information. I will present first asymptotic results concerning feasibility of this approach for large number of qubits. In particular I will discuss the witnessing power of entanglement polytopes for systems of large number of qubits. As finding entanglement polytopes, even for five qubits, is in fact intractable I will use the connection between the polytopes and the critical points of the linear entropy to provide at least brief characterization. This connection leads to a random matrix model involving Bernoulli ensemble. I will discuss preliminary implications of this model for the witnessing power of entanglement polytopes.

Uzy Smilansky (Rehovot, Israel)
E-Mail: Uzy.Smilansky@weizmann.ac.il
WWW page: http://www.weizmann.ac.il/complex/uzy
Affiliation: Department of Physics of Complex Systems, The Weizmann Institute of Science, Rehovot, 76100 IL
Title: The distribution of transit - times through metric (quantum) graphs
Abstract:
This work is motivated by an experiment which is now being carried out by Professor S Anlage in Maryland: A train of very short electromagnetic pulses is fed to a network of coaxial transmission lines through one vertex, and exit through another vertex. The times t it takes to cross the network is the transit time of interest here. We study the distribution of the transit times and show that asymptotically it falls off exponentially as A exp (- 𝜆 t) and explain how the constants A and 𝜆 depend on the network connectivity and the lengths of its edges.

Withdrawn due to illness of Valentin V. Sokolov (Novosibirsk, Russia)
E-Mail: valya.sokolov@gmail.com
Affiliation: Budker Institute of Nuclear Physics of SB RAS and Novosibirsk Technical University; Novosibirsk, Russia
Title: Neutron resonances: widths distribution versus the Porter-Thomas law
Abstract:
 

Jakub Zakrzewski (Cracow, Poland)
E-Mail: kuba@if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~kuba
Affiliation: M. Smoluchowski Institute of Physics Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland
Title: Many body localization with bosons
Abstract:
Many body localization (MBL) is typically studied in spin systems and/or for fermions in optical lattices. Bosons are avoided due to a large local Hilbert space in a lattice (a same site can be occupied by several particles). But we like difficult problems so we discuss MBL in such a setting. A particularly interesting case corresponds to bosons with random (repulsive) interactions [1]. The system in the noninteracting case reduces to free bosons in a periodic potential, i.e. is represented by extended Bloch states. The localization observed has thus a genuine interaction-based origin. We show that the system is characterized by an unusual mobility edge (with states of higher energy localizing easier), discuss possible approximate localization scenario. We consider also a standard model with disorder affecting the on-site energies (the chemical potential).

Marek Żukowski (Gdańsk, Poland)
E-Mail: fizmz@univ.gda.pl
Affiliation: Faculty of Mathematics, Physic and Informatics of the University of Gdansk, ul. Wita Stwosza 57, 80-952 Gdańsk, Poland
Title: Entanglement detection under noise for bright four mode squeezed vacuum and a new look at the polarization observables
Abstract:
New methods of correlation analysis in multi-photon quantum optics are introduced. They allow to construct much better entanglement witness (i.e., more resistant to noise and losses, and better working for stronger pump powers), and new more effective Bell inequalities. The inequalities are devoid of theoretical loopholes (i.e. additional assumptions, apart from local-realism/ causality). What is very important we have devised generalized methods which allow to find other entanglement conditions, which take as their starting point two-qubit entanglement indicators. The “headline” result of this line of research is the new approach to polarization correlation of quantum light in states of undefined intensities (or photon numbers). This leads to a revision of the concept of quantum Stokes observables. As a byproduct, we have found also new entanglement indicators involving standard quantum Stokes observables.

Karol Życzkowski (Warsaw, Poland)
E-Mail: karol@tatry.if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~karol/
Affiliation: nstitute of Physics, Jagiellonian University, ul Łojasiewicza 11, 30-348 Cracow, Poland and Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Random matrices and quantum dynamics: unitary, non-unitary and non-linear
Abstract:
Ensembles of random matrices useful to describe quantized chaotic dynamics in various setting are discussed and compared. Evolution operators for quantum unitary dynamics of a closed system are related to circular ensembles of Dyson, while typical non-unitary quantum maps, resulting from an interaction with an environment, correspond to ensembles of real non-hermitian matrices of the Ginibre ensemble. Furthermore, we discuss models of non-linear quantum evolution and analyze random matrices related to a matrix logistic map which are characterized by a fractal level density.