3rd Workshop on Quantum Chaos and Localisation Phenomena

25 - 27 May 2007 - Warsaw, Poland

Organising Committee
    * Szymon Bauch
    * Oleh Hul
    * Marek Ku¶
    * Micha³ £awniczak
    * Leszek Sirko - Chairman
    * Wanda Zawojska
    * Karol ¯yczkowski

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 3rd Workshop on Quantum Chaos and Localisation Phenomena will be held from May 25 to May 27, 2007 at the Institute of Physics of the Polish Academy of Sciences in Warszawa. Arrivals are planned on Friday, afternoon/evening (May 25). Departure will be on Sunday, May 27. Please disseminate information about the Workshop among your students, collaborators and colleagues who might be interested.

Second Announcement


Registration and Abstract Submission: April 15, 2007

Conference fee: 380 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 26, at 9 am.
-The poster session will be organized on Saturday. The posters will remain on display until 2.15 pm on Sunday, May 27. 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 - 265 PLN, a double room - 330 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 - 120 PLN, a double room - 170 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)
E-Mail: anlage@umd.edu
Affiliation: Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA
Title: Analog experiments on quantum chaotic scattering and transport

Collaborators: Thomas Antonsen, James Hart, Sameer Hemmady, Edward Ott, and Xing Zheng

The transport properties of mesoscopic and nanoscopic materials are dominated by quantum interference effects. Nevertheless it is challenging to delineate these effects through conventional transport experiments on real materials. Complications arise from finite temperatures (thermal smearing, inelastic scattering), and the excitation of two-level systems that can cause the electrons to decohere and drop out of the quantum-coherent transport process. We approach this problem from the perspective of nonlinear dynamics and utilize a unique experimental technique that directly simulates the quantum scattering properties of complicated (ray-chaotic) systems. A microwave cavity is used to simulate solutions to the time-independent Schrödinger equation for a two-dimensional ray-chaotic infinite square-well potential. The classically chaotic ray trajectories within a suitably shaped microwave cavity play a role analogous to that of the chaotic dynamics of noninteracting electron transport through a ballistic quantum dot in the absence of thermal fluctuations. Prior experimental work has examined the statistical properties of nearest-neighbor eigenvalue spacing [1], eigenfunctions [2], and the scattering and reaction matrices for 1- and 2-port single-channel systems [3]. In wave chaotic scattering, statistical fluctuations of the scattering matrix S and the impedance (reaction) matrix Z depend both on universal properties and on nonuniversal details of how the scatterer is coupled to external channels. We remove the non-universal effects of the coupling from the experimental S data using the radiation impedance obtained directly from the experiments [4], thus eliminating one of the most significant complications in conventional transport measurements. The Landauer-Büttiker formalism is applied to obtain the conductance of a corresponding mesoscopic quantum-dot device. We find good agreement for the probability density functions of the experimentally derived surrogate conductance [5], as well as its mean and variance, with the theoretical predictions based on random matrix theory [6]. We also observe a linear relation between the quantum dephasing parameter and the cavity ohmic loss parameter. The results apply to scattering measurements on any wave chaotic system. We also discuss future directions for this work.

[1] P. So, et al., Phys. Rev. Lett. 74, 2662 (1995).
[2] Dong-Ho Wu, et al., Phys. Rev. Lett., 81, 2890 (1998).
[3] S. Hemmady, et al., Phys. Rev. E 74, 036213 (2006).
[4] S. Hemmady, et al., Phys. Rev. Lett. 94, 014102 (2005).
[5] S. Hemmady, et al., Phys. Rev. B 74, 195326 (2006).
[6] P. W. Brouwer and C. W. J. Beenakker, Phys. Rev. B 55, 4695 (1997).

Andreas Buchleitner (Dresden)
E-Mail: abu@mpipks-dresden.mpg.de
Affiliation: Max-Planck-Institut für Physik komplexer Systeme, Nöthnitzer Strasse 38, D-01187 Dresden, Germany
Title: Entanglement in open quantum systems

We discuss the dynamical evolution of quantum entanglement under incoherent environment coupling, in various contexts. In particular, we discuss entanglement dynamics on a classically mixed regular chaotic phase space, and show that nonlinear resonances allow us to define generic, strongly entangled multipartite quantum states. The robustness of their multipartite entanglement increases with the particle number, i.e., in the semiclassical limit, for those classes of diffusive noise which assist the quantum-classical transition.

Giulio Casati (Como)
E-Mail: giulio.casati@uninsubria.it
Affiliation: Center for Nonlinear and Complex Systems, Universita' degli studi dell'Insubria- Via Valleggio, 11 - 22100 Como
Title: Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensates

To extract directed transport from random fluctuations is a problem at the heart of statistical mechanics with a long history, including links to the Maxwell demon. In far from equilibrium systems, in presence, for instance, of unbiased ac-driving, noise and dissipation, a directed transport, also known as ratchet effect, can be generated. The appearance of ratchet transport has recently gained renewed attention due to its possible relevance for biological transport, molecular motors and the prospects of nanotechnology. We demonstrate a quantum chaotic dissipative ratchet appearing for particles in a pulsed asymmetric potential in the presence of a dissipative environment. The system is characterized by directed transport emerging from a quantum strange attractor. This model exhibits, in the limit of small effective Planck constant, a transition from quantum to classical behavior, in agreement with the correspondence principle. We also discuss a model, consisting of two series of spatially periodic kicks, that offers a clear-cut way to implement directed transport with cold atoms in optical lattices. Finally, we discuss preliminary results for a periodically kicked Bose-Einstein condensate, where the ratchet effect stems from the mean-field interaction between the condensed atoms.

Valerie Doya (Nice)
E-Mail: valerie.doya@unice.fr
Affiliation: Laboratoire de Physique de la Matière Condensée, Université de Nice - CNRS (UMR 6622), Parc Valrose, 06108 Nice cedex 2 - France
Title: Scar selection in a chaotic optical fiber

In previous works, we proved that optical fibers constitute a favorable tool to investigate experimentally the wavefunctions of chaotic cavities. The ergodic behavior of the wavefuntions predicted by M.V. Berry and the enhancement of intensity associated to the scarring effect introduced by E. J. Heller have been observed in a D-shaped multimode fiber. The ergodic modes are generic whereas only some few modes exhibit localisation of light related to scar modes. With the aim to focus our experimental investigations on pure scar modes, a mechanism of scar modes selection in the fiber is required. Resting on recent results of localised modes selection in desordered systems using gain, we have introduced a localised gain region in the fiber. I will present our recent numerical results about the ability of the gain to perform a selective amplification of scar eigenmodes.

Piotr Garbaczewski (Opole)
E-Mail: pgar@uni.opole.pl
Affiliation: Institute of Physics, University of Opole, 45-052 Opole, Poland
Title: Information dynamics and origins of uncertainty

We carry out systematic study of uncertainty measures that are generic to dynamical processes of varied origins, provided they induce suitable continuous probability distributions. Their temporal properties are investigated with emphasis on thermodynamical patterns of behavior.

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: Experimental observation of 2D localized modes

In spite of two decades of intensive research, the experimental observation of strong localization of classical waves remains a tremendous challenge. One of the main difficulties lies in the fact that the signature of localization is sought after statistic measurements of transmission. Indeed, the expected exponential decrease of transmission could not be attributed unambiguously to localization rather than absorption. While localization, as proposed by Anderson may be defined as an inhibition of wave diffusion, a most stronger definition is that the eigenfunctions are characterized by an exponential decay in space. The increasing contribution of such long-lived modes, as time progresses, is responsible for the observed deviations from the regime of  purely diffusive transport. Besides the fact that their localized nature is not affected by absorption, exhibiting the localized modes inside the random system would be a direct demonstration of localization and the key to the understanding of the mechanism underlying the transition from diffusive to localized regime. Recently, we obtained unequivocal observations of localized modes in an open 2D random system and successfully confront them to numerical simulations and theoretical predictions. During my talk I will describe these experimental results and their analysis.

Achim Richter (Darmstadt)
Affiliation: Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
Title: Superscars and nodal domains in the barrier billiard

Intensity distributions of the electric field strength in a flat microwave billiard with a barrier inside [1] have been measured up to large mode numbers [2]. The following features are discussed: (i) a novel method for the reconstruction of the amplitudes and phases of the electric field strength distributions; (ii) the identification of the recently predicted superscars, i.e. eigenfunctions which are strongly localized around certain families of the periodic orbits, using the well known analogy between the electric field strength and the quantum mechanical wave functions in a two-dimensional microwave billiard; (iii) the determination of their physical properties, and (iv) the properties of the nodal domains in the barrier billiard, which are compared to model predictions [3, 4].

[1] E. Bogomolny and C. Schmit, Phys. Rev. Lett. 92, 244102 (2004).
[2] E. Bogomolny, B. Dietz, T. Friedrich, M. Miski-Oglu, A. Richter, F. Schäfer, and C. Schmit, Phys. Rev. Lett. 97, 254102 (2006).
[3] G. Blum, S. Gnutzmann, and U. Smilansky, Phys. Rev. Lett. 88, 114101 (2002).
[4] E. Bogomolny and C. Schmit, Phys. Rev. Lett. 88, 114102 (2002).

* Work supported by the Deutsche Forschungsgemeinschaft within the SFB634

Petr Seba (Prague)
E-Mail: seba@fzu.cz
Affiliation: Institute of Physics, Czech Academy of Sciences, Prague, Czech Republic
Title: Parking in the city

We discuss the spacing distribution between cars parked parallel to the curb. It has been shown recently that in the center of London this distribution is  astonishingly well described by the Gaussian Unitary Ensemble of random matrices. We present and simple theoretical model that explains this finding and compare its predictions with data collected in several Czech cities.

Hans-Jürgen Sommers (Essen)
E-Mail: h.j.sommers@uni-due.de
Affiliation: Fachbereich Physik, Universität Duisburg-Essen, Campus Essen, 45117 Essen, Germany
Title: Statistics of conductance and shot noise power in chaotic cavities

Collaborators: D. Savin, W. Wieczorek

We give analytic expressions for the distributions of conductance g and shot-noise power p for a chaotic cavity with arbitrary numbers of right and left channels n_1, n_2 and repulsion parameter \beta = 1, 2, 4. With the theory of Selberg's integral the first four cumulants of g and the first two cumulants of p are calculated for arbitrary n_1, n_2, beta. Also the asymptotics of the distributions near the edges are determined exactly up to linear order in distances from the edges. For g lying between 0 and 1 a power law for the conductance distribution is exact. All results are consistent, also with numerical simulations.

Bart Van Tiggelen (Grenoble)
E-Mail: bart.van-tiggelen@grenoble.cnrs.fr
Affiliation: CNRS/Laboratoire de Physique et Modelisation des Milieux Condeses, Universite Joseph Fourier, Maison des Magisteres, BP 166, F-38042 Grenoble Cedex 9, France
Title: Anderson Localization: 50 years minus epsilon......and counting

I this talk I will present a short state-of-the -art of Anderson Localization of waves. Almost 50 years after the pioneering paper, the subject no longer the unrecognizable monster that Anderson feared it to be in reviewing his creation after 25 yeras. It is more lively than ever, supported by  many astonishing experiments with light, sound and cold atoms. I will present the first dynamical experiment of 3D localization of ultrasound, carried out in the group of John Page, and a comparison to  a sophisticated  version of the  self-consistent theory of localization.

Jakub Zakrzewski (Cracow)
E-Mail: kuba@if.uj.edu.pl
Affiliation: M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland
Title: Double ionization in a strong laser field

I discuss a novel simplified model suitable for qualitative discussion of double ionization in strong laser pulses, confronting our model with the celebrated aligned electrons model. It is shown that the latter cannot describe simultaneous symetric electron escapes observed in recent experiments. Our model is free of that drawback and reproduces qualitatively the experimental momenta distributions. The details of time dynamics of the ionization process as well as its dependence on the symmetries of the initial state is discussed.

Contributed Talks

(Click on a name for more information)

Valerio Cappellini (Cracow)
E-Mail: valerio@cft.edu.pl
Affiliation: M. Smoluchowski Institute of Physics, Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland
Title: Classical limit of quantum dynamical entropies

Non-commutative dynamical entropies are studied in connection with the classical limit. For systems with a strongly chaotic classical limit, the Kolmogorov-Sinai invariant is recovered on time scales that are logarithmic in the quantization parameter. These quantum systems are not chaotic for any given finite quantization parameter, but become such after the classical limit has been performed; quantum entropy production analysis on logarithmic time scale provides us with a method to test their chaoticity directly on the quantum domain. The model of the quantized hyperbolic automorphisms of the 2--torus is examined in detail. The used techniques are based on a particular class of Coherent States on the torus, fulflling a very useful dynamical localization property.

Antonio M. Garcia-Garcia (Princeton)
E-Mail: ag3@Princeton.EDU
Affiliation: Department of Physics, Princeton University, Princeton, NJ 08544, USA
Title: Classical anomalous diffusion and quantum localisation: A new universality class in quantum chaos

Within the framework of the one parameter scaling theory we define a new universality class in quantum chaos based on the relation between classical anomalous diffusion and quantum power-law localization of the eigenstates. We study different systems such as the Harper model, kicked rotors with non-analytical potentials and Coulomb billiards, that fall inside this universality class. In all these cases the classical dynamics presents anomalous diffusion and the wavefunctions have power-law tails with an exponent controlled by the classical singularity. We determine in what circumstances the spectral and eigenfunctions correlations are similar to those of a disordered conductor at the Anderson transition. Based on our previous findings we describe how ultra cold atoms can be used to study experimentally the Anderson transition.

Oleh Hul (Warsaw)
E-Mail: olehhul@ifpan.edu.pl
Affiliation: Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland
Title: Investigation of quantum graphs and microwave networks

We present the results of numerical studies of parameter-dependent spectral statistics of quantum graphs with and without time-reversal symmetry. The change of the bonds lengths of the graph was chosen to be an external parameter. We calculated the autocorrelation functions of level velocities c(x) and c(w,x) as well as the distribution of avoided crossing gaps. Obtained results we compared with the predictions of the random matrix theory. We also present the experimental results for the distributions of the imaginary P(v) and the real P(u) parts of Wigner's reaction K matrix for irregular, tetrahedral graphs (networks) in the presence of absorption. In the experiment we used microwave networks, which were built of coaxial cables and attenuators connected by T-joints. Distributions of the imaginary and real parts of K matrix were obtained from the measurements of the scattering matrix S of the networks. We compare the experimental results with the theoretical predictions.

This work was partially supported by the Ministry of Education and Science grant No. N202 099 31/0746

Marian Rusek (Warsaw)
E-Mail: rusek@ifpan.edu.pl
Affiliation: Institute of Physics, Polish Academy of Sciences, 02-668 Warsaw, Poland
Title: Light localization in left handed media

Collaborators: Arkadiusz Or³owski and Jan Mostowski

Localized waves are orthogonal to all propagating waves. Thus they are composed of evanescent waves only [1]. Recently focusing of electromagnetic waves by left handed materials has attracted much attention [2-5]. It was suggested that "evanescent" waves in such a medium are in fact not evanescent at all: instead of decaying, their amplitude should actually grow up as they pass through a left-handed material. This unusual behavior of evanescent waves may modify the properties of localized waves. Thus a study of Anderson localization in disordered left handed materials seems interesting. The medium under consideration is studied using a generalized discrete-dipole approach. A generalization employed consists of simultaneous consideration of both magnetic and electric dipoles. The electric field radiated by magnetic dipoles acts on electric dipoles, and the magnetic field radiated by electric dipoles acts on magnetic dipoles. Of course, the dipoles of the same kind keep interacting with one another by a respective field as well. In the limit of large density of the dipoles as compared to the wavelength cubed their collection may be treated as an homogeneous material. Its dielectric and magnetic permeabilities are given by the well known Clausius-Mosotti formula. Suitable choice of the polarizabilities of electric and magnetic dipoles may make both permeabilities negative. Thus the resulting medium becomes a left handed one. We investigate this situation by simulating numerically a left handed lens built up of a collection of dipoles. According to the Clausius-Mosotti formula the product of density and polarizabilty is a constant. Thus in the limit of large density of dipoles the mean free path is much larger then the wavelength. As predicted by Ioffe-Regel's criterion, Anderson localization may happen when the mean free path becomes comparable to the wavelength. To investigate such a situation of strong disorder we resort to an (reasonable) approximation that individual dipoles represent macroscopic particles made of left handed material. We investigate the Anderson transition in the universal properties of the spectra of the scattering matrix [6]. It is a common belief that enhanced backscattering (or weak localization) is a precursor of the strong localization (formation of the band of localized waves). Therefore the ratio of the backscattering cone to the averaged background in left handed random media is also investigated.

[1] M. Rusek and A. Orlowski, Phys. Rev. E 59, 3655 (1999).
[2] J. B. Pendry, Phys. Rev. Lett. 85, 3966 (2000).
[3] G. V. 't Hooft, Phys. Rev. Lett. 87, 249701 (2001).
[4] J. M. Williams, Phys. Rev. Lett. 87, 249703 (2001).
[5] M. Nieto-Vesperinas and N. Garcia, Phys. Rev. Lett. 91, 099702 (2003).
[6] M. Rusek, J. Mostowski, and A. Orlowski, Phys. Rev. A 61, 022704 (2000).


Saturday, May 26

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

Invited Talks

9:05-9:40 Giulio Casati (Como, Italy)
Quantum ratchets for periodically kicked cold atoms and Bose-Einstein condensate

9:40-10:15 Bart van Tiggelen (Grenoble, France)
Anderson localization: 50 years minus epsilon... and counting

10:15-10:50 Fabrice Mortessagne (Nice, France)
Experimental observation of 2D localized modes

10:50-11:20 Coffee break

11:20-11:55 Andreas Buchleitner (Dresden, Germany)
Entanglement in open quantum systems

11:55-12:30 Piotr Garbaczewski (Opole, Poland)
Information dynamics and origins of uncertainty

12:30-13:05 Jakub Zakrzewski (Cracow, Poland)
Double Ionization in strong laser field

13:05-14:00 Lunch break

14:00-15:00 Poster Session

Contributed Talks

15:00-15:20 Valerio Cappellini (Cracow, Poland)
Classical limit of quantum dynamical entropies

15:20-15:40 Marian Rusek (Warsaw, Poland)
Light localization in left handed media

15:40-16:20 High tea (evening meal)

16:20 Warsaw tour and conference dinner

Sunday, May 27

Invited Talks

9:00-9:35 Achim Richter (Darmstadt, Germany)
Superscars and nodal domains in the barrier billiard

9:35-10:10 Valerie Doya (Nice, France)
Scar selection in a chaotic optical fiber

10:10-10:45 Petr Seba (Prague, Czech Republic)
Parking in the city

10:45-11:15 Coffee break

11:15-11:50 Hans Jürgen Sommers (Essen, Germany)
Statistics of conductance and shot noise power in chaotic cavities

11:50-12:25 Steven M. Anlage (College Park, USA)
Analog experiments on quantum chaotic scattering and transport

12:25-13:25 Lunch break

Contributed Talks

13:25-13:45 Antonio M. Garcia-Garcia (Princeton, USA)
Classical anomalous diffusion and quantum localisation: A new universality class in quantum chaos

13:45-14:05 Oleh Hul (Warsaw, Poland)
Investigation of quantum graphs and microwave networks

14:05-14:15 Closing remarks