Workshop on Quantum Chaos and Localisation Phenomena

4^th Workshop on Quantum Chaos and Localisation Phenomena

22 - 24 May 2009 - Warsaw, Poland

Organising Committee

    * Szymon Bauch
    * Oleh Hul
    * Marek Kuś
    * Michał Ławniczak
    * 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 4^th Workshop on Quantum Chaos and Localisation Phenomena will be held from May 22 to May 24, 2009 at the Institute of Physics of the Polish Academy of Sciences in Warszawa. Arrivals are planned on Friday, afternoon/evening (May 22). Departure will be on Sunday, May 24. Please disseminate information about the Workshop among your students, collaborators and colleagues who might be interested.

Second Announcement

Deadlines:

Registration and Abstract Submission: April 17, 2009

Conference fee: 430 PLN (100 Euro)

The conference fee includes two lunches, conference dinner, and social event on Saturday.
Limited number of grants for participants presenting posters will be available.

Scientific programme:

-The workshop's programme will consist of invited talks and poster contributions.
-Invited talks are allotted 35 minutes (including approx. 5 minutes
for questions/discussion).
-An overhead projector as well as a projector for a laptop will be available.
-The lectures will start on Saturday, May 23, at 9 am.
-The poster session will be organized on Saturday. The posters will remain on display until 2.15 pm on Sunday, May 24. 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

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 - 280 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 - 320 PLN, a double room - 400 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 - 130 PLN, a double room - 180 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)
* to be confirmed

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Steven M. Anlage (College Park)
E-Mail: anlage@umd.edu
Affiliation: Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
Title: Examination of short orbit deviations from Random Matrix Scattering Theory / E. Bradshaw(1), Jen-Hao Yeh(2), J. Hart(1), T. Antonsen(1,2), E. Ott(1,2), Steven M. Anlage(1,2), (1) Physics Department, University of Maryland, College Park, MD 20742-4111, (2) Electrical and Computer Engineering Department, University of Maryland, College Park, MD 20742-3285
Abstract:
We consider the effects of short orbits on the statistical properties of wave chaotic systems open to outside scattering channels. A theoretical expression for corrections to the scattering impedance is introduced and tested through a series of experiments on a thin ray-chaotic microwave cavity. The theory is found to provide a good description of non-universal effects due to short orbits in the experimental data. These results should be broadly useful in nuclear scattering, atomic physics, quantum transport in condensed matter systems, electromagnetics, acoustics, geophysics, etc.

Alexander Balanov (Loughborough)
E-Mail: A.Balanov@lboro.ac.uk
Affiliation: Department of Physics Loughborough University Loughborough LE11 3TU, United Kingdom
Title: Using chaotic miniband transport to control charge domain dynamics in semiconductor superlattices
Abstract:
We study the effects of a tilted magnetic field on the formation and motion of charge domains in a semiconductor superlattice and, as a result, on the properties of current oscillations. Previously, we found that tilting the magnetic field provides strong coupling between the Bloch and cyclotron motion of electrons within the lowest miniband. As a result, the electrons demonstrate a unique type of Hamiltonian chaos associated with an intricate mesh of conduction channels -- a stochastic web in the phase space -- leading to a large resonant increase in the current flow at critical values of the applied voltage. This phase-space patterning provides a sensitive mechanism for controlling the electrical resistance [1-3]. In my talk, I will show that the single-electron miniband chaos resulting from the interplay between cyclotron and Bloch oscillations has a dramatic effect on the collective electron dynamics by inducing complex propagating charge domain filaments and GHz-THz current oscillations. Shaping of the domain structure by the applied field increases both the power and the frequency of the associated electrical current oscillations.
[1] T.M. Fromhold et al., Nature 428, 726 (2004)
[2] D. Fowler et al., Phys. Rev. B. 76, 245303 (2007)
[3] A.G. Balanov et al., Phys. Rev. E. 77, 026209 (2008)

Andreas Buchleitner (Freiburg)
E-Mail: abu@uni-freiburg.de
Affiliation: Institute of Physics, Albert Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
Title: Microwave driven atoms: from Anderson localization to Einstein's photo effect
Abstract:
We study the counterpart of Anderson localization in driven one-electron Rydberg atoms. By changing the initial Rydberg state at fixed microwave frequency and interaction time, we numerically monitor the crossover from Anderson localization to the photo effect in the atomic ionization signal. Observation of this continuous transition is now in reach for laboratory experiments, in one single experimental setup.

Thomas Guhr (Duisburg – Essen)
E-Mail: thomas.guhr@uni-duisburg-essen.de
Affiliation: Fachbereich Physik, Universität Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany
Title: Superscars in billiards - a model for the doorway mechanism
Abstract:
In a unifying way, the doorway mechanism explains spectral properties in a rich variety of open mesoscopic quantum systems, ranging from atoms to nuclei. A distinct state and a background of usually chaotic other states couple to each other. This sensitively affects strength functions and other wave-function dependend statistics. The recently measured superscars in the barrier billiard provide an ideal model for an in--depth investigation of this mechanism. We introduce two new statistical observables, the full distribution of the maximum coupling coefficient to the doorway and directed spatial correlators. Using Random Matrix Theory and random plane waves, we obtain a consistent understanding of the experimental data.

Tsampikos Kottos (Middletown)
E-Mail: tkottos@wesleyan.edu
Affiliation: Department of Physics, Wesleyan University, Exley Science Tower, 265 Church Street, Middletown CT-06459, USA and MPI for Dynamics and Self-Organization, Bunsenstrasse 10, D-37073 Goettingen, Germany
Title: Probing Localization in Absorbing Systems via Loschmidt Echos
Abstract:
We measure Anderson localization in quasi-one-dimensional waveguides in the presence of absorption by analyzing the echo dynamics due to small perturbations. We specifically show that the inverse participation number of localized modes dictates the decay of the Loschmidt echo, differing from the Gaussian decay expected for diffusive or chaotic systems. Our theory, based on a random matrix modeling, agrees perfectly with scattering echo measurements on a quasi one-dimensional microwave cavity filled with randomly distributed scatterers.

Pavel Kurasov (Lund)
E-Mail: kurasov@maths.lth.se
Affiliation: Mathematics Centre for Mathematical Sciences, Lund Institute of Technology / Lund University, Box 118, SE-221 00 LUND
Title: Localization and quantum blockade on graphs and inverse problems for Aharonov-Bohm rings
Abstract:
Solution of the inverse scattering problem in the presence of Aharonov-Bohm magnetic field is discussed. We show that this problem has unique solution for simple rings, provided neither embedded eigenvalues, nor quantum blockade occur. It is discussed whether these conditions are necessary to guarantee the uniqueness.

Fabrice Mortessagne (Nice)
E-Mail: Fabrice.Mortessagne@unice.fr
Affiliation: Laboratoire de Physique de la Matière Condensée, Université de Nice - CNRS (UMR 6622), Parc Valrose, 06108 Nice cedex 2 - France
Title: Statistics of eigenfunctions in chaotic open systems: a random matrix approach
Abstract:
The effects of losses in wave systems with Time Reversal Symmetry is well known: modes with infinite lifetime and real eigenfunctions are turned into resonances with finite lifetimes and complex eigenfunctions. While statistical properties of spectral widths of open chaotic systems are nowadays well understood from isolated resonances to strong overlapping regime, a statistical description of eigenfunction complexness is still missing. I will present recent results concerning the properties of eigenfunctions in the isolated resonance regime through a unique statistical parameter called the complexness factor.

Achim Richter (Darmstadt)
E-Mail: richter@ikp.tu-darmstadt.de
Affiliation: Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany, and the European Centre for Theoretical Studies in Nuclear Physics and Related Areas, I-38100 Villazzano (Trento), Italy
Title: Double-slit experiments in microwave billiards with regular and chaotic dynamics
Abstract:
We are presently performing double-slit experiments with two-dimensional microwave billiards of regular and chaotic dynamics, respectively [1]. The experiments were stimulated by work of Casati and Prosen [2] who investigated numerically the interference pattern behind the double-slit caused by the leakage of a wave packet originating from within a quantum billiard. They showed that the interference pattern depends on the billiard geometry. In recent experiments with water surface waves [3] stationary patterns are observed but these cannot really distinguish between effects due to the regular and chaotic dynamics in the two billiards, respectively. We attack the problem with microwaves by exciting the two billiards (i) with a single point-like antenna emitting microwaves at fixed frequency and (ii) with a linear array of emitting antennas. In the first case we observe a clear dependence of the interference patterns on the billiard geometry. For the second case a directed wave packet is excited by combining successively measured frequency spectra. The time evolution of the electromagnetic wave packet will then provide a further way of studying the predicted dependence of the interference pattern on the billiard geometry.
Supported by the DFG within the SFB 634.
[1] S. Bittner, B. Dietz, M. Miski-Oglu, P. Oria Iriarte, A. Richter, and F. Schäfer, to be published.
[2] G. Casati and T. Prosen, Phys. Rev. A 72, 032111 (2005).
[3] Y. Tang, Y. Shen, J. Yang, X. Liu, J. Zi, and B. Li, Phys. Rev. E 78, 047201 (2008).

Krzysztof Sacha (Kraków)
E-Mail: krzysztof.sacha@uj.edu.pl
Affiliation: Instytut Fizyki, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
Title: Anderson localization of a center of mass of a Bose-Einstein condensate
Abstract:
Bose-Einstein condensate can exhibit Anderson localization in a disorder potential if particle interactions are sufficiently weak. Then both the profile of a particle cloud and the probability density for a center of mass of the cloud are exponentially localized. We show that it is possible to realize systems where the particle density profile is not affected by a weak disorder and still the center of mass reveals Anderson localization. We consider quantum bright and dark solitons in a Bose-Einstein condensate and show that the probability density for soliton positions can be exponentially localized in a disorder potential.

Petr Seba (Prague)
E-Mail: seba@fzu.cz
Affiliation: Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
Title: The universality distribution of distances in the human and animal traffic: random matrix or not?
Abstract:
We show that the mechanism of distance perception which is evolutionarily very old and shared with mammals and birds leads finally to an universal behavior of spacings in the human/animal traffic. We demonstrate this fact on data referring to car parking and stopping, highway and pedestrian traffic, bird perching on electric poles and the distances within a sheep herd. A simple theory of this phenomenon will be presented.

Hans-Jürgen Stöckmann (Marburg)
E-Mail: stoeckmann@physik.uni-marburg.de
Affiliation: Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
Title: Scattering properties of chaotic microwave resonators
Abstract:
To study the properties of a system such as its spectrum it has to be opened leading to a modification of the system properties. Thus every measurement unavoidably gives an unwanted combination of the properties of the system and the apparatus. Scattering theory is the method of choice to cope with this situation. Originally developed in nuclear physics [1], it meanwhile has found numerous applications also in mesoscopic systems [2]. An example is the study of the transport properties of open quantum dots. These measurements, however, are difficult: (i) it is non-trivial determine the confining potential from the geometry of the gate electrodes, (ii) impurities are unavoidable and difficult to control, (iii) the systems typically are of sub-micron size, and (iv) temperatures of the order of mK or even lower are needed. Here microwave resonators pose an alternative. For flat resonators there is a complete equivalence to the corresponding quantum dot system, as long as electron-electron interactions are negligible [3]. System sizes are of the order of centimeter, the measurements can be performed at room temperature, and the geometry is perfectly controllable. Furthermore, a detailed look into the system is possible, whereas standard quantum dot techniques only allow the study of global transport properties. I shall illustrate these features of the microwave technique by three examples. First, results on the emission patterns of deformed micro-resonators will be presented. Shape optimization to enhance emission in given directions is a topical research subject in optoelectronics. Using microwaves the size of the resonators is promoted from the micron to the centimeter regime because of the much larger wavelengths of the microwaves as compared to those in the optical regime. From scanning probe microscopy studies it is known that the electron flow through quantum contacts does not show the diffraction pattern which might have been expected from elementary quantum mechanics but exhibiters an intricate branching structure instead [4]. It had been conjectured by Kaplan [5] that these features are a manifestation of caustics generated by the background potential due to impurities and charged donors. In a microwave realisation of the flow through a potential landscape we had been able to verify the caustics conjecture, where the potential had been mimicked by a variation of the resonator height. The result may be applied as well to the wave patterns produced in the ocean giving new insight into the formation of rogue waves. In the last part I shall present some recent results on the analysis of the poles of the scattering matrix in the regime of strong overlap. There are numerous results on average quantities in open systems such as distribution and correlation functions of reflection and transmission coefficients. The direct measurement of the poles, however, had not been accessible up to now. Here a recent progress had been achieved by using the method of Harmonic Inversion [6]. In this technique poles and residua of the scattering matrix are obtained from the eigenvalues of a matrix which can be generated from the experimental spectra. No foreknowledge on the number of contributing eigenvalues is needed for this purpose. First results on the distributions of linewidths in the regime of strong overlap are presented.
[1] T. Guhr, A. Mueller-Groeling, H. Weidenmueller, Phys. Rep. 299, 189 (1998)
[2] C. Beenakker, Rev. Mod. Phys. 69, 731 (1997)
[3] H.-J. Stoeckmann, Quantum Chaos - An Introduction, Cambridge University Press 1999
[4] M. Topinka et al., Science 289, 183 (2000)
[5] L. Kaplan, Phys. Rev. Lett. 89, 184103 (2002)
[6] J. Main, Phys. Rep. 316, 233 (1999)

Gregor Tanner (Nottingham)
E-Mail: gregor.tanner@nottingham.ac.uk
Affiliation: School of Mathematical Sciences, University of Nottingham, University Park, Nottingham, NG7 2RD, UK
Title: Quantum searches and quantum communication on networks
Abstract:
Quantum search algorithms both within an ordered list or on an extended network are based on propagating a well known initial state into a target state in order N^{1/2} steps (where N is the number of items or nodes). I will review the basic algorithms introduced by Grover and Kempe, Ambianis and others and amke the link to quantum graphs. I will then offer a new interpretation of the search process in terms of avoided crossings and localised `defect' states and show how this mechanism can be used to facilitate multi-search algorithms and to build communication channels between distinct nodes based only on wave interference.

Karol Życzkowski (Warszawa)
E-Mail: karol@tatry.if.uj.edu.pl
Affiliation: Center for Theoretical Physics, Polish Academy of Sciences, 02-668 Warszawa, Poland
Title: Quantum chaos and non unitary dynamics
Abstract:
A link between properties of quantized chaotic systems and random matrices will be reviewed. Statistical properties of periodically driven quantum chaotic systems described in a finite dimensional Hilbert space {\cal H}_N can be described by circular ensembles of random unitary matrices. To describe the effect of a possible interaction of the system in question with an environment one needs to work with density operators, which are Hermitian, positive and normalized. Discrete time evolution of a density matrix can be represented by so-called quantum operation (completely positive, trace preserving map). We introduce several ensembles of {\sl random operations}, discuss algorithms to generate them and investigate spectral properties of the corresponding superoperators with spectrum consisting of $N^2$ eigenvalues inside the unit disk. A quantum analogue of the Frobenius-Perron theorem concerning the spectrum of stochastic matrices is formulated. Obtained predictions for random operations are compared with spectral properties of quantized chaotic systems, interacting with an environment.

Contributed Talks

(Click on a name for more information)
* to be confirmed

Wojciech Bruzda (Kraków)
E-Mail: wojtek@gorce.if.uj.edu.pl
Affiliation: Instytut Fizyki, Jagiellonian University, ul. Reymonta 4, 30-059 Kraków, Poland
Title: Spectral gap & relaxation to equilibrium in open quantum systems
Abstract:
We investigate several types of quantum maps, describing evolution of open quantum systems. Generically for a given map there exists a unique invariant state $\omega$, such that $\Phi\omega=\omega$. The relaxation time at which any initial state converges to $\omega$ is governed by the spectral gap of the corresponding superoperator. The size of the spectral gap is studied for a class of modified quantum baker maps and compared with the properties of a random quantum system. For a typical quantum chaotic system exponential convergence to the equilibrium is reported.

Oleh Hul (Warszawa)
E-Mail: olehhul@ifpan.edu.pl
Affiliation: Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warszawa, Poland
Title: Investigation of graphs with absorption / O. Hul, M. Ławniczak, S. Bauch, P. Seba(2) and Leszek Sirko, Institute of Physics, Polish Academy of Sciences, Aleja Lotników 32/46, 02-668 Warsaw, Poland, (2) Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
Abstract:
We present the results of numerical and experimental study of hexagon graphs (networks) in the presence of absorption. One-port and two-port scattering matrices were studied. In the experiment we used microwave networks of coaxial cables connected by joints. Absorption of microwave networks can be changed by introducing of microwave attenuators into its bonds. In the numerical calculations absorption inside the cables was described by complex wave vector, while attenuators were modeled by optical potentials. In order to investigate universal scattering properties of graphs one should remove direct processes. This can be done by using radiation impedance approach. We present both experimental and numerical results and compare it with theoretical predictions.
This work was partially supported by the Ministry of Science and Higher Education grant N202 099 31/0746.

Vyacheslav Shatokhin (Freiburg)
E-Mail: vs81@physik.uni-freiburg.de
Affiliation: Institute of Physics, Albert Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
Title: Deducing residual enhancement in coherent backscattering of light from two atoms
Abstract:
Coherent backscattering of intense laser light by cold atoms is considered. I will discuss the earlier predicted effect of residual self-interference of inelastically scattered photons, and show how to observe this effect with two atoms confined in an optical lattice.

Thomas Wellens (Freiburg)
E-Mail: thomas.wellens@physik.uni-freiburg.de
Affiliation: Institute of Physics, Albert Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany
Title: Nonlinear coherent transport of waves in disordered media
Abstract:
In general, transport of waves in disordered media cannot fully be described as a simple diffusion process, since wave interference effects lead to a reduction or even complete suppression of the diffusion constant (weak or strong localization) and the appearance of a coherent backscattering peak. In this talk, I present a diagrammatic theory for treating the impact of nonlinearities on coherent backscattering. The theory is applied to describe propagation of weakly interacting Bose-Einstein condensates in disordered potentials, on the one hand, and multiple scattering of light in nonlinear media, on the other one. In particular, the conditions under which nonlinear effects diminish or enhance the height of the coherent backscattering peak are discussed. Finally, I also talk about the possibility to incorporate quantum-mechanical many- particle effects (for example multi-photon scattering processes from strongly driven two-level atoms), which generally lead to decoherence, thereby affecting the disorder-induced localization effects.

Programme

Saturday, May 23

9:00-9:05 Leszek Sirko (Warsaw, Poland)

Opening

INVITED TALKS

9:05-9:40 Achim Richter (Darmstadt, Germany)

Double-slit experiments in microwave billiards with regular and chaotic dynamics

9:40-10:15 Thomas Guhr (Duisburg, Germany)

Superscars in billiards - A model for the doorway mechanism

10:15-10:50 Fabrice Mortessagne (Nice, France)

Statistics of eigenfunctions in chaotic open systems: a random matrix approach

10:50-11:25 Alexander Balanov (Loughborough, UK)

Using chaotic miniband transport to control charge domain dynamics in semiconductor superlattice

11:25-12:00 coffee break

12:00-12:35 Petr Šeba (Prague, Czech Republic)

The universality distribution of distances in the human and animal traffic: random matrix or not?

12:35-13:10 Pavel Kurasov (Lund, Sweden)

Localization and quantum blockade on graphs and inverse problems for Aharonov-Bohm rings

13:10-13:45 Karol Życzkowski (Cracow, Poland)

Quantum chaos and non-unitary dynamics

13:45- 14:45 lunch break

14:45-16:00 POSTER SESSION

CONTRIBUTED TALKS

16:00-16:20 Wojciech Bruzda (Cracow, Poland)

Spectral gap and relaxation to equilibrium in open quantum systems

16:20-16:40 Thomas Wellens (Freiburg, Germany)

Nonlinear coherent transport of waves in disordered media

16:40 Warsaw tour and conference dinner

Sunday, May 24

INVITED TALKS

9:00-9:35 Hans-Jürgen Stöckmann (Marburg, Germany)

Scattering properties of chaotic microwave resonators

9:35-10:10 Steven M. Anlage (College Park, USA)

Examination of short orbit deviations from Random Matrix Scattering Theory

10:10-10:45 Gregor Tanner (Nottingham, UK)

Quantum searches and quantum communication on networks

10:45-11:15 coffee break

11:15-11:50 Andreas Buchleitner (Freiburg, Germany)

Microwave driven atoms: from Anderson localization to Einstein's photo effect

11:50-12:25 Krzysztof Sacha (Cracow, Poland)

Anderson localization of a center of mass of a Bose-Einstein condensate

12:25-13:00 Tsampikos Kottos (Middletown, USA)

Probing localization in absorbing systems via Loschmidt echos

13:00-14:00 lunch break

CONTRIBUTED TALKS

14:00-14:20 Slava Shatokhin (Freiburg, Germany)

Deducing residual enhancement in coherent backscattering of light from two atoms

14:20-14:40 Oleh Hul (Warsaw, Poland)

Investigation of graphs with absorption

14:40-14:50 Closing remarks