5th Workshop on Quantum Chaos and Localisation Phenomena May 20–22, 2011, Warsaw, Poland organised by Institute of Physics Polish Academy of Sciences, Center for Theoretical Physics Polish Academy of Sciences, and Pro Physica Foundation PROGRAMME Organising Committee Szymon Bauch ([email protected]) Sunday, May 22 Oleh Hul ([email protected]) INVITED TALKS Marek Kuś ([email protected]) 9:00–9:35 Uzy Smilansky (Rehovot, Israel) Michał Ławniczak ([email protected]) Stationary scattering from a nonlinear network Leszek Sirko – chairman ([email protected]) 9:35–10:10 Yan V. Fyodorov (Nottingham, UK) Level curvature distribution at the spectral edge of random Hermitian matrices 10:10–10:45 Pavel Kurasov (Stockholm, Sweden) Magnetic Schrödinger operators on graphs: spectra, Objectives inverse problems and applications 10:45–11:20 Karol Życzkowski (Warsaw, Poland) To assess achievements and to formulate directions of new research Level spacing distribution revisited on quantum chaos and localisation 11:20–11:50 coffee break To bring together prominent experimental and theoretical physicists 11:50–12:25 Andreas Buchleitner (Freiburg, Germany) who share a common interest in quantum chaos and localisation Transport, disorder, and entanglement phenomena 12:25–13:00 Jan Kˇríž (Hradec Králové, Czech Republic) Chaos in the brain 13:00–13:35 Agn`es Maurel (Paris, France) Experimental study of waves propagation using Fourier Transform Profilometry Scope 13:35–14:30 lunch break CONTRIBUTED TALKS Presentations will focus on the following topics: 14:30–14:50 Filip Studniˇcka (Hradec Králové, Czech Republic) Quantum chaos and nonlinear classical systems Analysis of biomedical signals using differential geometry invariants Quantum and microwave billiards 14:50–15:10 Michał Ławniczak (Warsaw, Poland) Quantum and microwave graphs Investigation of Wigner reaction matrix, cross- and velocity Atoms in strong electromagnetic fields – experiment and theory correlators for microwave networks Chaos vs. coherent effects in multiple scattering 15:10–15:30 Maciej Janowicz (Warsaw, Poland) Anderson localisation Quantum properties of coupled generalized logistic map Random lasers lattices Quantum chaos and quantum computing 15:30–15:40 Closing remarks Entanglement and noise PROGRAMME INVITED TALKS Friday, May 20 Fading statistics in communications – a random 19:00–21:00 Welcome party matrix approach Saturday, May 21 Jen-Hao Yeh, Thomas Antonsen, Edward Ott, Steven M. Anlage 9:00–9:10 Leszek Sirko (Warsaw, Poland) Opening Physics Department, University of Maryland, College Park, MD 20742-4111, USA INVITED TALKS 9:10–9:45 Achim Richter (Darmstadt, Germany) Fading is the observation of variations in signal strength measured at Simulating graphene with a microwave photonic crystal a receiver due to time-dependent variations in the propagation of waves 9:45–10:20 Steven M. Anlage (College Park, USA) from the source, or due to multi-path scattering and interference. It is Fading statistics in communications – a random matrix well known that the quantitative statistical theory of wave chaos – random approach matrix theory (RMT) – can be successfully applied to predict statistical 10:20–10:55 Jakub Zakrzewski (Cracow, Poland) properties of many quantities, such as the scattering matrix, of a wave Extraction of information from dynamics for strongly chaotic system. Here we start from the statistical model of the scatter- correlated systems ing matrix [1] to establish a general fading model. The model provides 10:55–11:30 Heinerich Kohler (Madrid, Spain) a first-principles understanding of the most common statistical model used Fidelity in chaotic and random systems in the communications field, namely Rayleigh fading, and shows that the statistical properties are governed by a single quantity related to the loss 11:30–12:00 coffee break or de-phasing parameter of RMT. We also combine the RMT fading 12:00–12:35 Dima Shepelyansky (Toulouse, France) model with our random coupling model (RCM) that takes into account Wigner crystal in snaked nanochannels system-specific features such as direct and short orbits [2–4], to build 12:35–13:10 Bart van Tiggelen (Grenoble, France) a more general fading model that includes Rician fading. In the high 3D Anderson localization of ultrasound and cold atoms loss-parameter limit, our model agrees with the Rayleigh/Rice models, 13:10–13:45 Gregor Tanner (Nottingham, UK) however it shows significant deviations from the Rayleigh/Rice distribu- Wave intensity distributions in complex structures tion in the limit of low loss. We have performed experiments with two ray-chaotic microwave cavities [3,4] to test the RMT/RCM fading model 13:45–14:45 lunch break over a wide range of loss parameter values. 14:45–16:00 POSTER SESSION Work funded by the ONR/Maryland AppEl Center Task A2 (contract No. CONTRIBUTED TALKS N000140911190), the AFOSR under grant FA95500710049. 16:00–16:20 Lock Yue Chew (Singapore) [1] P.W. Brouwer, C.W.J. Beenakker, Phys. Rev. B 55, 4695 (1997). The quantum signature of chaos through the dynamics [2] James A. Hart, T.M. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009). of entanglement [3] Jen-Hao Yeh et al., Phys. Rev. E 81, 025201(R) (2010). 16:20–16:40 Adam Sawicki (Warsaw, Poland and Bristol, UK) [4] Jen-Hao Yeh et al., Phys. Rev. E 82, 041114 (2010). Scattering from isospectral graphs 16:40 Warsawtourandconferencedinner 1 INVITED TALKS NOTES Transport, disorder, and entanglement Andreas Buchleitner Quantum optics and statistics, Institute of Physics, Albert-Ludwigs University of Freiburg, Hermann-Herder-Str. 3, D-79104 Freiburg, Germany In many areas of physics we witness dramatic differences between classical and quantum transport – from the theory of charge or heat con- duction in the solid state, over radiation transport in multiple scattering media, to energy transport in various scenarios of light-matter interaction. In general, we expect quantum features to fade away on large scales, due to the ever more unavoidable – and detrimental – influence of the envi- ronment which scrambles relative phases and damps quantum amplitudes. Recent experimental evidence suggests, however, that the functional ef- ficiency of large biomolecular units may stem from quantum coherence phenomena, despite strong environment coupling. We explain such ef- ficiency, under the assumption that evolution is able to steer finite size three dimensional systems into molecular conformations with optimal co- herent transport properties. It turns out that such optimal conformations are characterized by specific, optimal entanglement properties between different sites of the molecular complex. 2 PARTICIPANTS AND AUTHORS INVITED TALKS Bart van Tiggelen (invited speaker), p. 12 CNRS/Laboratoire de Physique et Modelisation des Milieux Condeses, Universite Level curvature distribution at the spectral edge Joseph Fourier, Maison des Magisteres, BP 166, F-38042 Grenoble Cedex 9, of random Hermitian matrices France e-mail: [email protected] Yan V. Fyodorov Mathematical Physics, School of Mathematical Sciences, Tomasz Tkocz (co-author), p. 14 University of Nottingham, NG72RD Nottingham, UK Dept. of Physics, Warsaw University, Hoża 69, 00-681 Warsaw, Poland Level curvature is a measure of sensitivity of eigenvalues of a disor- Maciej Wołoszyn (poster), p. 42 dered/chaotic system to perturbations. In the bulk of the spectrum Random Matrix Theory predicts the probability distributions of level curvatures Dept. of Applied Informatics and Computational Physics, AGH University to be given by Zakrzewski–Delande expressions. Motivated by growing of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland interest in statistics of extreme (maximal or minimal) eigenvalues of dis- e-mail: [email protected] ordered systems of various nature, it is natural to ask about the associated level curvatures. I show how calculating the distribution for the curva- Jen-Hao Yeh (co-author), p. 1 tures of extreme eigenvalues in GUE ensemble can be reduced to study- Physics Dept., Univ. of Maryland, College Park, MD 20742-4111, USA ing asymptotics of orthogonal polynomials appearing in a recent work by e-mail: [email protected] Nadal and Majumdar. The corresponding asymptotic analysis being yet outstanding, I instead will discuss solution of a related, but somewhat Jakub Zakrzewski (invited speaker), p. 13 simpler problem of calculating the level curvature distribution averaged over all the levels in a spectral window close to the edge of the semicircle. M. Smoluchowski Institute of Physics Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland e-mail: [email protected] Karol Życzkowski (invited speaker), p. 14 Center for Theoretical Physics, Polish Academy of Sciences, al. Lotników 32/46, 02-668 Warszawa, Poland e-mail: [email protected] 50 3 INVITED TALKS PARTICIPANTS AND AUTHORS Andrzej L. Sobolewski (co-author), p. 38 Fidelity in chaotic and random systems Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland Heinerich Kohler e-mail: [email protected] Instituto de Ciencia de Materiales de Madrid, CSIC, Spain Bartłomiej Spisak (poster), p. 41 Fidelity is the overlap of a wave function, propagated by a Hamil- Dept. of Applied Informatics and Computational Physics, AGH University tonian in time, with the same initial wave function, propagated by a per- of Science and Technology, Al. Mickiewicza 30, 30-059 Cracow, Poland turbed wave function. Its behavior depends crucially on the choice of the e-mail: [email protected] initial wave function. In the talk we review two cases: If the initial state is random a simple analytic relation with parametric spectral correlations can be established. Filip Studniˇcka (contributed talk), p. 21 The latter can easier be measured, since no knowledge of the wave func- University of Hradec Kralove, Rokitanskeho 62, CZ-500 03 Hradec Kralove, tion is required. On the other hand, if the initial state is an eigenstate of Czech Republic the unperturbed system we find unexpected features like non-ergodicity. e-mail: fi[email protected] In this case fluctuations become important and the full fidelity distribu- tion (FFD) becomes a non-trivial function.