6th Workshop on Quantum Chaos and Localisation Phenomena

24 - 26 May 2013 - Warsaw, Poland

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

Organising Committee
    * Szymon Bauch
    * Oleh Hul
    * Marek Kuś
    * Michał Ławniczak
    * Paweł Masiak
    * Leszek Sirko - Chairman

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 6th Workshop on Quantum Chaos and Localisation Phenomena will be held from May 24 to May 26, 2013 at the Institute of Physics of the Polish Academy of Sciences in Warszawa. Arrivals are planned on Friday, afternoon/evening (May 24). Departure will be on Sunday, May 26. Please disseminate information about the Workshop among your students, collaborators and colleagues who might be interested.

Second Announcement


Registration and Abstract Submission: April 22, 2013

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) to the bank account:

BPH o/Warszawa
PL 77 1060 0076 0000 3210 0014 4494
Swift code: BPHKPLPK
Instytut Fizyki PAN, Warszawa
Chaos6, 2013

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 25, at 9 am.
-The poster session will be organized on Saturday. The posters will remain on display until Sunday, May 26. 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: 31 July 2013.

Hotel information:

Gromada Hotel **
ul. 17-go Stycznia 32, 02-148 Warszawa
tel. +48 (22) 576 46 00
fax +48 (22) 846 15 80
(Hotel is located in the nearest vicinity of the airport.
Approximated price for workshop's participants - a single room - 299 PLN, a double room - 329 PLN)

Centrum Kulturalne Ojców Barnabitów *
(The Cultural Centre of the Barnabite Fathers)
ul. Smoluchowskiego 1, 02-679 Warszawa
tel. +48 (22) 543 20 01, 543 23 02
fax: +48 (22) 543 22 82
e-mail: centrum.kulturalne@wp.pl
(Prices: a single room - 308 PLN, a double room - 363 PLN)

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 - 133 PLN, a double room - 182 PLN)

* - 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)

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 Time-Reversal in a Wave Chaotic System
 Exploiting the time-reversal invariance and reciprocal properties of the lossless wave equation enables elegantly simple solutions to complex wave-scattering problems and is embodied in the time-reversal mirror. In previous work, we extended the concepts of Loschmidt Echo and Fidelity to classical waves, such as acoustic and electromagnetic waves, to realize a new sensor paradigm. Here we demonstrate the implementation of an electromagnetic time-reversal mirror in a wave chaotic system containing a discrete nonlinearity. We demonstrate that the time-reversed nonlinear excitations reconstruct exclusively upon the source of the nonlinearity. As an example of its utility, we demonstrate a new form of secure communication and point out other applications. This work was funded by the IC-Postdoctoral program (Grant No. 20101042106000), the ONR AppEl Center Task A2 (No. N000140911190), the AFOSR (No. FA95500710049), and the Maryland Center for Nanophysics and Advanced Materials.

Ram Band (Bristol, UK)
WWW page: http://www.maths.bris.ac.uk/~maxrb/
Affiliation: Mathematics Dept., Univ. of Bristol, Howard House, University of Bristol, Queens Avenue, Bristol BS8 1SN, UK
Title: Universality of the momentum band density of periodic graphs
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic network. We show that this probability exhibits universal properties. More precisely, the probability to be in the spectrum does not depend on the edge lengths (as long as they are generic) and is also invariant within some classes of graph topologies. Based on a joint work with Gregory Berkolaiko.

Andreas Buchleitner (Freiburg, Germany)
WWW page: http://www.mpipks-dresden.mpg.de/mpi-doc/buchleitnergruppe/start.html
Affiliation: Quantum optics and statistics, Institute of Physics, Albert-Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
Title: Nonmonotonic quantum-to-classical transition in multiparticle interference
Quantum-mechanical wave–particle duality implies that probability distributions for granular detection events exhibit wave-like interference. On the single-particle level, this leads to self-interference—e.g., on transit across a double slit—for photons as well as for large, massive particles, provided that no which-way information is available to any observer, even in principle. When more than one particle enters the game, their specific many-particle quantum features are manifested in correlation functions, provided the particles cannot be distinguished. We are used to believe that interference fades away monotonically with increasing distinguishability—in accord with available experimental evidence on the single- and on the many-particle level. We demonstrate experimentally and theoretically that such monotonicity of the quantum-to-classical transition is the exception rather than the rule whenever more than two particles interfere. As the distinguishability of the particles is continuously increased, different numbers of particles effectively interfere, which leads to interference signals that are, in general, nonmonotonic functions of the distinguishabilityof the particles.

Giulio Casati (Como, Italy)
Affiliation: Center Complex Systems - Insubria University Como, Via Valleggio, 11 -22100 Como Italy
Title: Conservation Laws and Thermodynamic Efficiencies
The understanding of the microscopic mechanisms which determine the macroscopic laws of heat and particles transport is one of the main problems of statistical mechanics. On the other hand, thermoelectric phenomena, which involve the conversion between thermal and electrical energy, and provide a method for heating and cooling materials, are expected to play an increasingly important role in meeting the energy challenge of the future. Here we discuss a new approach to this problem, which is rooted in nonlinear dynamical systems. More precisely we will discuss idealized models of interacting particles in one and two dimensions.

Oleh Hul  (Warsaw, Poland)
E-Mail: @olehhul@ifpan.edu.pl
Affiliation: Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Isoscattering quantum graphs and microwave networks
Can one hear the shape of a graph from outside? This is a modification of the famous question of Mark Kac "Can one hear the shape of a drum?" which can be asked in the case of scattering systems such as quantum graphs and microwave networks. It addresses an important mathematical problem whether scattering properties of such systems are uniquely connected to their shapes? We present the first experimental approach to this problem in the case of microwave networks simulating quantum graphs. We discuss the scattering from a pair of isospectral microwave networks consisting of vertices connected by microwave coaxial cables. The networks are extended to scattering systems by connecting leads to infinity in a way preserving their symmetry to form isoscattering networks. We show that the concept of isoscattering graphs is not only a theoretical idea but it could be realized experimentally. [This work was supported by the Ministry of Science and Higher Education grant No. N N202 130239.]

Heiner Kohler (Madrid, Spain)
Affiliation: Dept. of Theory and Simulation of Materials, Instituto de Ciencias de Materiales de Madrid, Sor Juana Ines de la Cruz 3, Cantoblanco, 28049 Madrid, Spain
Title: Asymmetry induced localization transition
We investigate a two-level system (TLS), which couples via non-commuting operators to two independent oscillator baths. In equilibrium the renormalized hopping matrix element is finite when the coupling is symmetric even for infinitely strong coupling strength. The two level system is in a delocalized phase. For finite coupling strength a localization transition occurs for a critical asymmetry angle, which separates the localized from the delocalized phase. Using the method of flow equations we are also able to monitor real time dynamics.

Pavel Kurasov (Stockholm, Sweden)
WWW page: http://www2.math.su.se/~pak/
Affiliation: Mathematical Institute, Stockholm University, 106 91 Stockholm, Sweden
Title: Spectral gap for quantum graphs and their connectivity
Spectral gap for discrete graphs is sometimes called algebraic connectivity due to its close relation to vertex and edges connectivities. We study the spectral gap for quantum graphs in relation to graph's connectivity. First of all using Euler's theorem we prove, that among all graphs having the same total length the spectral gap is minimal for the graph formed by one edge. Moreover we show that in contrast to discrete graphs connection between the connectivity and the spectral gap is not one-to-one. The size of the spectral gap depends not only on the topology of the metric graph but on its geometric properties as well. It is shown that adding suffciently large edges as well as cutting away suffciently small edges leads to a decrease of the spectral gap. Corresponding explicit criteria are given. [This is a joint work with G. Malenova and S. Naboko.]

Rafael Mendez-Sanchez (Cuernavaca, Mexico)
Affiliation: Instituto de Ciencias Físicas, Universidad Nacional Autónoma de México P.O. Box 48-3, 62251 Cuernavaca Mor., Mexico
Title: Experimental studies in quasi 1D elastic rods
A revision of recent experimental results on the vibrations of elastic systems is given. In locally periodic rods, which have approximate invariance under translations, constructed joining $N$ unit cells, the spectrum shows bands and gaps whereas the wave amplitudes are extended. When defects are introduced the states are localised and different phenomena are observed. When the defects are chosen with certain rule the Wannier-Stark Ladders are obtained; when the defects are random, Anderson localisation is observed. All these effects were found for closed systems but the introduction of absorbers allows to mimic open scattering systems. In this case quasi-1D cavities can be constructed and the reflection amplitude, including its phase, can be measured. In all cases analyzed excellent agreement between theory and experiment is obtained.

Achim Richter (Darmstadt, Germany)
WWW page: http://www.ikp.tu-darmstadt.de/gruppen_ikp/achimrichter/achimrichtercv.en.jsp
Affiliation: Institut für Kernphysik, Technische Universität Darmstadt D-64289 Darmstadt, Germany
Title: Dirac-Microwave Billiards, Photonic Crystals and Graphene
In the Workshop on Quantum Chaos and Localization Phenomena, May 20 – 22, 2011 in Warsaw, Poland I have spoken about our first experiments and modeling grapheme with photonic crystals. In my talk in the present 6th Workshop I will, after recapitulating the analogy between two-dimensional nonrelativistic (Schrödinger) and relativistic (Dirac) quantum billiards and microwave billiards, discuss in detail e.g. the band structure, the local density of states at the Dirac point, its relation to the scattering matrix and its use for determining the experimental length spectrum of periodic orbits in the relativistic regime around the Dirac point and in the non-relativistic one away from it, and the effect of edge states on the behavior of the mean density of states as function of quasimomentum. Finally it is shown how the logarithmic divergency of states at the so called Van Hove singularities can be interpreted as a Lifshitz topological phase transition. [Supported by the DFG within the SFB 634]

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: Shifts of resonance widths as a probe of eigenfunction nonorthogonality
Resonances feature themselves in the energy-dependent S matrix as its poles in the complex energy plane. They can be analytically described as the complex eigenvalues of an effective non-Hermitian operator. Notably, the associated resonance wavefunctions are known to be non-orthogonal that has many important applications, ranging from nuclear physics, to quantum optics and solid state. In this talk, I will consider an open (scattering) quantum system under the action of a perturbation of its closed counterpart. It is demonstrated that the resulting shift of resonance widths is a sensitive indicator of the non-orthogonality of resonance wavefunctions, being zero only if those were orthogonal. Focusing further on chaotic systems, I will introduce a new type of parametric statistics in open systems, and derive (within random matrix theory) the distribution of the resonance width shifts in the regime of weakly open system. [Based on a joint work with Yan Fyodorov (QMUL).]

Adam Sawicki (Warsaw, Poland)
Affiliation: Center for Theoretical Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: N-particle quantum statistics on graphs
I will show how to develop a full characterization of abelian quantum statistics on graphs. We explain how the number of anyon phases is related to connectivity. I will show the independence of quantum statistics with respect to the number of particles for 2-connected graphs. For non-planar 3-connected graphs bosons and fermions will be identified as the only possible statistics, whereas for planar 3-connected graphs I will show that one anyon phase exists. The approach also yields an alternative proof of the structure theorem for the first homology group of n-particle graph configuration spaces. This is a joint work with Jonathan Harrison, Jon Keating and Jonathan Robbins.

Christos Skiadas (Crete, Greece)
E-Mail: skiadas@cmsim.net
Affiliation: Technical University of Crete
Title: Local stable or unstable regions in 2-dimensional chaotic forms: Examples and simulations
We analyze 2-dimensional chaotic forms resulting from very simple systems based on two chaotic characteristics that is rotation and parallel movement or translation in geometric terms. Reflection is another alternative, along with rotation, for several interesting chaotic formations.Rotation and translation are very common types of movements in the world around us. It is worth noting to explore the chaotic or non-chaotic forms arising from these two main generators. The rotation–translation chaotic case presented is based on the theory analyzed in the book —Chaotic Modeling and Simulation: Analysis of Chaotic Models, Attractors and Forms and in the paper CHAOTIC MODELING AND SIMULATION IN ROTATION–TRANSLATION MODELS. An overview of the chaotic flows in rotation–translation is given. It is observed the presence of chaos when discrete rotation-translation equation forms are introduced. Instead the continuous equations analogue of the discrete cases is useful to find the trajectories of chaotic flows. Characteristic cases and illustrations of chaotic attractors and forms are analyzed and simulated. The analysis of chaotic forms and attractors of the models presented is given along with an exploration of the characteristic or equilibrium points. Applications in the fields of Astronomy-Astrophysics (Galaxies), Chaotic Advection (the sink problem) and Von Karman streets are presented.

Uzy Smilansky (Rehovot, Israel)
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: Transmission through noisy graphs
We study the transmission of waves through quantum graphs which are subject to time dependent random noise. This way we model e.g., graphs with fluctuating bond lengths. We obtain expressions for the noise averaged transmission coefficients, and in particular, study the effects of the noisy environment on resonance transmission.

Valentin Sokolov (Novosibirsk, Russia)
E-Mail: V.V.Sokolov@inp.nsk.su
Affiliation: Budker Institute of Nuclear Physics of SB RAS and Novosibirsk Technical University; Novosibirsk, Russia
Title: Mesoscopic quantum transport in presence of a weakly disordere background: time delay, decoherence and energy absorption
Effect of a disordered many-body environment is analyzed on the chaotic dynamics of a quantum particle in a mesoscopic ballistic structure. The decoherence and energy absorption phenomena are treated on the same footing within the framework of a microscopic model based on the general theory of the resonance scattering. The single-particle doorway resonance states excited in the structure via external channels are damped not only because of the escape onto such channels but also due to ulterior population of the long-lived background states. The latter broadens the delay time distribution thus strongly enhancing the time delay inside the system. As a result, transmission through the structure splits up into incoherent sum of the flow formed by the interfering damped doorway resonances and the retarded flow of the particles re-emitted by the environment back in the structure. The resulting internal energy absorption as well as the decoherence rate are uniquely expressed in terms of the spreading width that controls coupling to the background.

Hans-Jürgen Stöckmann (Marburg, Germany)
WWW page: https://for760.tu-dresden.de/Action/ShowUser/Hans-J%C3%BCrgen%20St%C3%B6ckmann
Affiliation: Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
Title: Microwave studies of complex scattering systems
Most of the phenomena observed for waves are universal and can be found likewise in water, sound, and electromagnetic waves as well as in wave mechanics. Using microwave techniques it thus becomes possible to study e.g. questions by means of classical waves which originally had been conceived in the context of quantum mechanics. This will be illustrated by a number of examples such as the study of a microwave analogue of graphene, or the transport of microwaves through a potential landscape simulating the situation in the ocean.

Sandro Wimberger (Heidelberg, Germany)
E-Mail: s.wimberger@thphys.uni-heidelberg.de
Affiliation: Institute for theoretical Physics, Heidelberg University, Philosophenweg 19, D-69120, Heidelberg, Germany
Title: Taming quantum chaos in the many-body Wannier-Stark system
Modern quantum and atom-optical experiments allow for an unprecedented control of microscopic degrees of freedom, not just in the initialization but also in the dynamical evolution of quantum states. This talk focuses on the dynamics of ultra-cold bosons in optical lattice structures. Results are reported on the interband transport in a tilted lattice, i.e. a cold-atoms realization of the famous Wannier-Stark problem. Single-particle and mean-field experimental investigations motivate our many-body Bose-Hubbard model for the system.

Jakub Zakrzewski (Cracow, Poland)
E-Mail: kuba@if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~kuba
Affiliation: Instytut Fizyki im. Mariana Smoluchowskiego, Uniwersytet Jagielloñski, ul. Reymonta 4, PL-30-059 Kraków, Poland
Title: Many-body Anderson loalization in one dimensional systems
The problem of Anderson loalization of interating partiles is revisited. We demonstrate, using quasi-exact numerical simulations, that Anderson localization in a disordered one-dimensional potential survives in the presence of attrative interation between partiles. The loalization length of the partiles enter of mass - computed analytially for weak disorder - is in good agreement with the quasi-exact numerial observations using the Time Evolving Block Decimation algorithm. Comparison with previously developed mean field desription of the problem is made. Our approach allows for a simulation of the entire experiment including the final measurement of all atom positions.

Karol Zyczkowski (Warsaw, Poland)
E-Mail: karol@tatry.if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~karol/
Affiliation: agiellonian University and Center for Theoretical Physics, PAS
Title: Random quantum states and random unitary matrices associated with a graph
For a class of graphs consisting of m vertices one defines an ensemble of random pure states on a composite system with m subsystems of the same dimension n. Each edge of the graph represents a random unitary matrix of size n^2 distributed according to the Haar measure, which describes an unknown interaction between the subsystems. For a given topology of the graph we analyze statistical properties of the corresponding ensemble of quantum pure states and the ensemble of structured random unitary matrices of size N=n^m. [Joint work with Pawel Kondratiuk]


Friday, May 24

19:00-22:00 Welcome party (Gromada Hotel - Turquoise Room)

Saturday, May 25

9:00-9:10 Leszek Sirko (Warsaw, Poland)



9:10-9:45 Achim Richter (Darmstadt, Germany)

Dirac-Microwave Billiards, Photonic Crystals and Graphene

9:45-10:20 Hans-Jürgen Stöckmann (Marburg, Germany)

Microwave studies of complex scattering systems

10:20-10:55 Steven M. Anlage (College Park, USA)

Nonlinear Time-Reversal in a Wave Chaotic System

10:55-11:30 Rafael Mendez (Cuernavaca, Mexico)

Experimental studies in quasi 1D elastic rods

11:30-12:00 coffee break

12:00-12:35 Giulio Casati (Como, Italy)

Conservation Laws and Thermodynamic Efficiencies

12:35-13:10 Jakub Zakrzewski (Cracow, Poland))

Many-body Anderson localization in one dimensional systems

13:10-13:45 Andreas Buchleitner (Freiburg, Germany)

Nonmonotonic quantum-to-classical transition in multiparticle interference

13:45- 14:45 lunch break

14:45-16:00 POSTER SESSION


16:00-16:20 Sandro Wimberger (Heidelberg, Germany)

Taming quantum chaos in the many-body Wannier-Stark system

16:20-16:40 Oleh Hul (Warsaw, Poland)

Isoscattering quantum graphs and microwave networks

16:40 Warsaw tour and conference dinner

Sunday, May 26


9:00-9:35 Uzy Smilansky (Rehovot, Israel)

Transmission through noisy graphs

9:35-10:10 Pavel Kurasov (Stockholm, Sweden)

Spectral gap for quantum graphs and their connectivity

10:10-10:45 Karol Życzkowski (Warsaw and Cracow, Poland)

Random quantum states and random unitary matrices associated with a graph

10:45-11:20 Valentin V. Sokolov (Novosibirsk, Russia)

Mesoscopic quantum transport in presence of a weakly disordered background: time delay, decoherence and energy absorption

11:20-11:50 coffee break

11:50-12:25 Christos H. Skiadas (Chania, Crete, Greece)

Local stable or unstable regions in 2-dimensional chaotic forms: Examples and simulations

12:25-13:00 Dmitry Savin (London, UK)

Shifts of resonance widths as a probe of eigenfunction nonorthogonality

13:00-13:35 Heinerich Kohler (Madrid, Spain)

Asymmetry induced localization transition

Many-body Anderson localization in one dimensional systems

13:35-14:30 lunch break


14:30-14:50 Rami Band (Bristol, UK)

Universality of the momentum band density of periodic graphs

14:50-15:10 Adam Sawicki (Warsaw, Poland and Bristol, UK))

N-particle quantum statistics on graphs

15:10-15:20 Closing remarks


Invited Speakers: