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3rd Workshop on Quantum Chaos and Localisation Phenomena
25 - 27 May 2007 - Warsaw, Poland
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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.
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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.
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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.
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Second Announcement
Deadlines:
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.
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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)
E-Mail:richter@ikp.tu-darmstadt.de
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.
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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).
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Program
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
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