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7th Workshop on Quantum Chaos and Localisation Phenomena
29 - 31 May 2015 - Warsaw, Poland
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Organisers
* Institute of Physics, Polish Academy of Sciences
* Center for Theoretical Physics, Polish Academy of Sciences
* Pro Physica Foundation
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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 7th Workshop on Quantum Chaos and Localisation Phenomena
will be held from May 29 to May 31, 2015 at the Institute of Physics of the Polish Academy of Sciences in Warszawa.
Arrivals are planned on Friday, afternoon/evening (May 29). Departure will be on Sunday (May 31) evening or on Monday (June 1)
morning if necessary.
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 26, 2015
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) or Euros to the bank account:
Bank Gospodarstwa Krajowego
Account number for PLN 89 1130 1017 0013 4373 9820 0025
Account number for Euros 35 1130 1017 0013 4373 9820 0027
SWIFT GOSKPLPW
Instytut Fizyki PAN, Warszawa
Chaos7
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 30, at 9 am.
-The poster session will be organized on Saturday.
The posters will remain on display until Sunday, May 31.
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: 15 August 2015.
Hotel information:
Airport Hotel Okęcie **
ul. 17-go Stycznia 32, 02-148 Warszawa
tel. +48 (22) 456 80 81
fax +48 (22) 456 80 29
(Hotel is located in the nearest vicinity of the airport.
Approximated price for workshop's participants - a single room - 220 PLN, a double room - 260 PLN including breakfast)
Centrum Barnabitów*
(The Barnabite Centre)
ul. Smoluchowskiego 1, 02-679 Warszawa
tel. +48 (22) 543 20 01, 543 23 02
fax: +48 (22) 543 22 82
e-mail: info@barnabici.pl
(Prices: a single room - 178 PLN, a double room - 228 PLN, apartment 347 including breakfast)
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.
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Invited Speakers
(Click on a name for more information)
* to be confirmed
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: Focusing Waves at Arbitrary Locations in a Ray-Chaotic Enclosure Using Semi-Classical Analysis
Abstract:
Time-reversal invariance of the lossless wave equation allows reconstruction of collapsing waveforms in a ray-chaotic scattering environment utilizing a single-channel time-reversal mirror [1 - 2]. However, a typical time reversal experiment requires that a transmitter be initially present at the target focusing point, which limits the application of this technique. We have extended the Random Coupling Model (RCM) to include the effects of short orbits on the statistical properties of wave chaotic systems with non-universal features [3 - 6]. By combining the semi-classical description of short orbits with the time-reversal mirror, we can make a waveform appear at an arbitrary location in a complex scattering environment. Specifically, we use knowledge of the billiard geometry and a semi-classical ray algorithm to calculate the signal that would be received at a transceiver port resulting from the injection of a short pulse at the desired target location [7]. The time-reversed version of this signal is then injected into the transceiver port and an approximate reconstruction of the short pulse is created at the target. We experimentally demonstrate the method using a microwave billiard and quantify the reconstruction quality as a function of enclosure loss, port coupling and other considerations. The reconstruction quality is predicted by the statistics of the scattering-parameter S21^2 between the transceiver and target points in the enclosure. This work was funded by the Office of Naval Research (contracts No. N00014130474 and N000141512134), and the Center for Nanophysics and Advanced Materials (CNAM). [1] Steven M. Anlage, John Rodgers, Sameer Hemmady, James Hart, Thomas M. Antonsen, Edward Ott, Acta Physica Polonica A 112, 569 (2007). [2] Matthew Frazier, Biniyam Taddese, Thomas Antonsen, Steven M. Anlage, Phys. Rev. Lett. 110, 063902 (2013). See "Alice and Bob Go Nonlinear" Synopsis on Physics.APS.org. [3] James A. Hart, T. M. Antonsen, E. Ott, Phys. Rev. E 80, 041109 (2009). [4] Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, Phys. Rev. E 81, 025201(R) (2010). [5] Jen-Hao Yeh, James Hart, Elliott Bradshaw, Thomas Antonsen, Edward Ott, Steven M. Anlage, Phys. Rev. E 82, 041114 (2010). [6] Jen-Hao Yeh, Thomas M. Antonsen, Edward Ott, Steven M. Anlage, Phys. Rev. E 85, 015202(R) (2012). [7] Bo Xiao, Thomas M. Antonsen, Edward Ott, and Steven M. Anlage, “Focusing Waves at an Arbitary Location in a Ray-Chaotic Enclosure Using Time-Reversed Synthetic Sonas.” arXiv:1409.3850
Andreas Buchleitner (Freiburg, Germany)
E-Mail: abu@uni-freiburg.de
WWW page: http://www.mpipks-dresden.mpg.de/mpi-doc/buchleitnergruppe/start.html
Affiliation: Dept. for Quantum Optics and Statistics, Institute of Physics & Freiburg Institute for Advanced Studies, Albert Ludwigs University of Freiburg, Hermann-Herder-Str. 3D-79104 Freiburg, Germany
Title: A statistical benchmark for BosonSampling
Abstract:
Computing the state of a quantum mechanical many-body system composed of indistinguishable particles distributed over a multitude of modes is one of the paradigmatic test cases of computational complexity theory: Beyond well-understood quantum statistical effects, the coherent superposition of many-particle amplitudes rapidly overburdens classical computing devices -essentially by creating extremely complicated interference patterns, which also challenge experimental resolution. With the advent of controlled many-particle interference experiments, optical set-ups that can efficiently probe many-boson wave functions - baptised BosonSamplers - have therefore been proposed as efficient quantum simulators which outperform any classical computing device, and thereby challenge the extended Church-Turing thesis, one of the fundamental dogmas of computer science. However, as in all experimental quantum simulations of truly complex systems, there remains one crucial problem: How to certify that a given experimental measurement record is an unambiguous result of sampling bosons rather than fermions or distinguishable particles, or of uncontrolled noise? We describe a statistical signature of many-body quantum interference, which can be used as an experimental (and classically computable) benchmark for BosonSampling.
Barbara Dietz-Pilatus (Darmstadt, Germany)
E-Mail: dietz@ikp.tu-darmstadt.de
WWW page:
Affiliation: Technische Universität Darmstadt, Institut für Kernphysik, Schlossgartenstraße 9, 64289 Darmstadt, Germany
Title: Experiments with Superconducting Microwave Resonators Emulating Artificial Graphene and Fullerene C60
Abstract:
We determined experimentally the eigenvalues of quantum billiards with the shapes of a rectangle and of Africa, respectively,that contain circular scatterers forming a triangular grid, so-called Dirac billiards. For this, high-precision measurements have been performed with superconducting microwave billiards. We investigated the particular features of the density of the eigenvalues (DOE), which resembles that of a graphene flake, and of their fluctuation properties. I will demonstrate in my talk that the van Hove singularities, that show up as sharp peaks in the DOE, divide the associated band into regions where the system is governed by the non-relativistic Schrödinger equation of the quantum billiard and the Dirac equation of the graphene billiard of corresponding shape, respectively. Furthermore, experiments have been performed using a spherical superconducting microwave resonator with the geometric structure of the C60 fullerene molecule in order to, firstly, study with very high resolution the exceptional spectral properties emerging from the symmetries of the icosahedral structure of the carbon lattice. Secondly, we determined the number of zero modes with eigenvalues at the Dirac point to test the predictions of the Atiyah-Singer index theorem, which relates it to the topology of the curved carbon lattice. * Supported by the DFG within the Collaborative Research Center CRC634
Thomas Guhr (Duisburg-Essen, Germany)
E-Mail: thomas.guhr@uni-due.de
WWW page:
Affiliation: Faculty of Physics, University of Duisburg-Essen, Lotharstr. 1, 47048 Duisburg, Germany
Title: Chaotic Scattering: Exact Results and Microwave Experiments
Abstract:
Chaotic Scattering is relevant in many areas of physics, from nuclei and mesoscopic systems to telecommunication. While the whole scattering matrix is assumed to be random in the Mexico approach, only the Hamiltonian of the interaction zone is modelled by a random matrix in the Heidelberg approach. We solve a long-standing problem in the Heidelberg approach: we calculate the distribution of the off-diagonal scattering elements exactly. We also carry out a comparison with data from microwave experiments.
Jiri Lipovsky (Hradec Kralove, Czech Republic)
E-Mail: jiri.lipovsky@uhk.cz
WWW page:
Affiliation: Department of Physics, Faculty of Science, Rokitanskeho 62, 500 03 Hradec Kralove, Czech Republic
Title: How to find the effective size of a non-Weyl graph
Abstract:
We study the asymptotics of the number of resolvent resonances in a quantum graph with attached halflines. It has been proven that in some cases the constant by the leading term of the asymptotics (the effective size of the graph) is smaller than one expects by the Weyl law, since some resonances escape to infinity. We show how to find this effective size by the method of pseudo orbit expansion. Furthermore, we prove two theorems on the effective size of certain type of graphs with standard (Kirchhoff) coupling.
Michał Ławniczak (Warsaw, Poland)
E-Mail: lawni@ifpan.edu.pl
WWW page:
Affiliation: Institute of Physics, Polish Academy of Sciences, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Study of the power spectra and the elastic enhancement factor for chaotic quantum systems
Abstract:
We present the results of the experimental study of the power spectra S(f) of discrete and finite series of eigenenergies for quantum and microwave graphs and billiards. Quantum graphs were simulated by microwave networks. It is possible because the one-dimensional Schrödinger equation, describing the wave functions on graph bonds, is analogical to the Telegraph equation describing the electric potentials on network bonds. The rectangular and chaotic microwave cavities simulate quantum regular and chaotic billiards, respectively. The analogy between quantum and microwave billiards is based upon the equivalency of the Schrödinger equation the Helmholtz equation. Our results indicate that the power spectra can be used as an experimental measure of chaoticity of such systems. We also present the results of a study of the elastic enhancement factor W(S) for partially chaotic and chaotic quantum billiards simulated by rectangular and rough microwave cavities in the case of preserved time reversal symmetry.
Ville Maisi (Zurich, Switzerland)
E-Mail: vmaisi@phys.ethz.ch
WWW page:
Affiliation: Laboratory for Solid State Physics, ETH Zurich 8093 Zurich, Switzerland
Title: Out of equilibrium measurements on a quantum dot: determination of the equilibrium free energy and an experimental test of the Jarzynski equality
Abstract:
Equilibrium thermodynamics is a fundamental branch of physics providing tools to make predictions of macroscopic many-particle systems independent of detailed microscopic processes governing their properties. In the recent trend towards smaller systems, which deviate strongly from the thermodynamic limit, fluctuations departing from the equilibrium state often become prominent and non-equilibrium dynamics needs to be taken into account. We investigate a single discrete energy level, a fundamental building block in quantum mechanics, in a GaAs/AlGaAs quantum dot coupled to a single thermal and electron reservoir by using single-electron counting techniques [1]. The device we use is presented in Fig. 1 (a). By applying a voltage ramp to a plunger gate electrode, we change the chemical potential of the electrons in the dot and thus perform work and change the internal energy of the system. We demonstrate that with a fast drive, the system is driven out of equilibrium. By utilizing the so-called Jarzynski equality [2] we show that the result of our non-equilibrium measurement is predicted by an equilibrium property, the free energy. Since our system consists essentially of a single discrete electronic state and it is possible to realize controllably tens of thousands of repetitions of the drive protocol, our experiments provide a controllable and precise test of the free energy extraction based on the Jarzynski equality. In a second set of experiments we employ feedback in the drive protocol as shown in Figs. 1 (b) and (c). If an excess electron resides in the quantum dot, we bring its chemical potential high so that it tunnels out quickly. When the excess electron is out of the dot, we drive the chemical potential down so that an electron is taken into the dot. Such a feedback protocol allows us to determine the tunnel dynamics of the system efficiently. With this technique we demonstrate, that the quantum dot we use, has doubly degenerate energy levels due to spin for the first eight electrons taken into the dot. We also probe the energy dependence of the tunnel coupling as well as perform exited state spectroscopy with the feedback technique. References [1] A. Hofmann et al, arXiv 1504.04949 (2015) [2] C. Jarzynski, Phys. Rev. Lett. 78, 2690 (1997).
Sebastian Müller (Walk Bristol, U.K.)
E-Mail: sebastian.muller@bristol.ac.uk
WWW page:
Affiliation: School of Mathematics University of Bristol University, Walk Bristol BS8 1TW, U.K.
Title: Spectral statistics of chaotic many-body systems
Abstract:
We investigate the spectral statistics chaotic many-body systems, using a trace formula that expresses the level density of chaotic many-body systems as a smooth term plus a sum over contributions associated to solutions of the nonlinear Schrödinger equation. Our formula applies to bosonic systems with discrete sites, such as the Bose-Hubbard model, in the semiclassical limit as well as in the limit where the number of particles is taken to infinity. The focus of the talk will be to investigate the two point correlation function of the level density by studying interference between solutions of the nonlinear Schr\"odinger equation. We show that in the limits taken the statistics of fully chaotic many-particle systems becomes universal and agrees with predictions from the Wigner-Dyson ensembles of random matrix theory. We also discuss the effect of discrete geometric symmetries on this statistics for the example of the Bose-Hubbard model without disorder. The conditions for Wigner-Dyson statistics involve a gap in the spectrum of the Frobenius-Perron operator, leaving the possibility of different statistics for systems with weaker chaotic properties.
Włodzimierz Piechocki (Warsaw, Poland)
E-Mail: Wlodzimierz.Piechocki@ncbj.gov.pl
WWW page:
Affiliation: Dept. of Fundamental Research, National Centre for Nuclear Research, ul. Hoża 69, 00-681 Warsaw, Poland
Title: Level spacing distribution of the Bianchi IX model
Abstract:
Our results concern quantum chaos of the vacuum Bianchi IX model. We apply the equilateral triangle potential well approximation to the potential of the Bianchi IX model to solve the eigenvalue problem for the physical Hamiltonian. Such approximation is well satisfied in vicinity of the cosmic singularity. Level spacing distribution of the eigenvalues is studied with and without applying the unfolding procedure. In both cases, the obtained distributions are qualitatively described by Brody's distribution, revealing some sort of the level repulsion. The observed repulsion may reflect chaotic nature of the classical dynamics of the Bianchi IX universe.
Luca Salasnich (Padova, Italy)
E-Mail: luca.salasnich@pd.infn.it
WWW page:
Affiliation: Dept. of Physics and Astronomy "Galileo Galilei", Univ. of Padova, Via Marzolo 8, 35131 Padova, Italy
Title: Dimensional reduction and localization of a Bose-Einstein condensate in a quasi-1D bichromatic optical lattice
Abstract:
From the 3D Gross-Pitaevskii equation we derive an effective 1D Gross-Pitaevskii equation which is used to study different aspects of the localization of a Bose-Einstein condensate made of dilute and ultracold alkali-metal atoms and confined in a one-dimensional bichromatic quasiperiodic optical-lattice potential. Our numerical results suggest the breaking of localization induced by a sufficiently strong repulsion generated by a positive inter-atomic scattering length.
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:
Abstract:
Uzy Smilansky (Rehovot, Israel)
E-Mail: Uzy.Smilansky@weizmann.ac.il
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: Dysons Brownian Motion Model for Random Matrix Theory - Revisited
Abstract:
In his 1962 paper, F. Dyson introduced a then novel approach for studying random matrix ensembles in terms of Brownian dynamics in the space of matrices. He then proposed a Fokker-Planck evolution for the spectral distribution function, whose stationary solution provides the spectral joint probability distribution function P. Here, we reformulate the approach for the traces, and derive the Fokker-Planck equations and the joint probability distribution Q. Advantages of this version of Dyson's theory will be discussed, and a few new identities between traces will be derived.
Valentin V. Sokolov (Novosibirsk, Russia)
E-Mail: valya.sokolov@gmail.com
WWW page:
Affiliation: Budker Institute of Nuclear Physics of SB RAS and Novosibirsk Technical University; Novosibirsk, Russia
Title: ELASTIC ENHANCEMENT FACTOR: MESOSCOPIC SYSTEMS VERSUS MACROSCOPIC 2D ELECTROMAGNETIC ANALOGOUS DEVICES
Abstract:
Excess of probabilities of the elastic processes over the inelastic ones is a common feature of the resonance scattering processes that are described with the aid of the random matrix theory (RMT). Quantitatively, this phenomenon is characterized by the elastic enhancement factor F that is a typical ratio of elastic and inelastic cross sections. Being measured experimentally, this quantity can supply us with important information about the character of the complicated states formed on the intermediate stage of a resonance reaction. Generally speaking, this factor depends on the number M of scattering channels as well as on the channel's transmission coefficients T. However, when the number of channels is very large, what is typical of the processes such as, for example, the resonance nuclear reactions, the enhancement factor is entirely controlled by the only parameter η = MT that changes in very wide bounds (Verbaarschot's regime). On the contrary, in the macroscopic analogous experiments with 2D irregularly shapedelectromagnetic resonators, that are widely used to mimic the chaotic quantum dynamics, the number of channels is very restricted. In this case the enhancement factor depends on the number of channels and on transmission coefficients separately. We juxtapose the two specified regimes in detail. We demonstrate that complete analytical solution valid for any fixed number M of equivalent channels with arbitrary transmission coefficients 0 < T < 1 is possible in the case of the systems without time-reversal symmetry. More than that, in the practically significant case of only two scattering channels, M = 2, influence of the absorption due to ohmic losses can also be described analytically. Meanwhile, no explicit analytical results can be derived in the case of a T-invariant device. Therefore we have used numerical methods to be able to demonstrate the similarity as well as distinctions between these two cases.
Hans-Jürgen Stöckmann (Marburg, Germany)
E-Mail: stoeckmann@physik.uni-marburg.de
WWW page:
Affiliation: Fachbereich Physik, Philipps-Universität Marburg, Renthof 5, D-35032 Marburg, Germany
Title: Spectral properties of microwave graphs with local absorption
Abstract:
The influence of absorption on the spectra of microwave graphs has been studied experimentally [1]. The microwave networks were made up of coaxial cables and T junctions. First, absorption was introduced by attaching a 50 Ohm load to an additional vertex for graphs with and without time-reversal symmetry. The resulting level-spacing distributions were compared with a generalization of the Wigner surmise in the presence of open channels proposed recently by Poli et al. [2]. A good agreement was found using an effective coupling parameter. Secondly, absorption was introduced along one individual bond via a variable microwave attenuator, and the influence of absorption on the length spectrum was studied. The peak heights in the length spectra corresponding to orbits avoiding the absorber were found to be independent of the attenuation, whereas the heights of peaks belonging to orbits passing the absorber once or twice showed the expected decrease with increasing attenuation. [1] Allgeier etal, PRE 89, 022925 (2014), [2] Poli et al, Phys. Rev. Lett. 108, 174101 (2012)
Juan Diego Urbina (Regensburg, Germany)
E-Mail: juan-diego.urbina@physik.uni-regensburg.de
WWW page:
Affiliation: Institut für Theoretische Physik Universität Regensburg, 93040 Regensburg, Germany
Title: The semiclassical approximation in Fock space: interactions, interference, and quantum signatures of field chaos
Abstract:
We will review recent developments in the rigorous construction of semiclassical approximations for interacting bosonic systems, in the spirit of Gutzwiller where the quantum mechanical time evolution operator is written as a coherent sum over the real solutions of some classical equations. After briefly presenting our derivation of the quantum-field analog of the van Vleck-Gutzwiller propagator, we show how it can be used to predict a new kind of many-body phenomena due to interference in many-body space which, contrary to wave interference, are not affected by the presence of interactions and their characteristic non-linear effect in the classical mean field equations. In a further development, a trace formula that associates long-wavelength oscillations in the smoothed many-body density of states with specific types of solutions of non-linear wave equations in the lattice will be derived, and possible applications will be discussed.
Jakub Zakrzewski (Cracow, Poland)
E-Mail: kuba@if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~kuba
Affiliation: M. Smoluchowski Institute of Physics Jagiellonian University, ul. Reymonta 4, PL-30-059 Cracow, Poland
Title: Cold atom motivated models with off-diagonal disorder
Abstract:
A well known problem of one dimensional tight binding model in the presence of disorder leading to Anderson localization is reconsidered. A binary disorder is assumed to be created by immobile heavy particles for the motion of the lighter, mobile species in the limit of no interaction between mobile particles. Fast periodic modulations of interspecies interactions allow us to produce an effective model with small diagonal and large off-diagonal disorder unexplored in cold atoms experiments. We present an expression for an approximate Anderson localization length and verify the existence of the well known extended resonant mode. We also analyze the influence of nonzero next-nearest neighbor hopping terms. We point out that periodic modulation of interaction allow disorder to work as a tunable band-pass filter for momenta. We discuss also the impact of off-diagonal disorder on Bose glass formation for interacting particles.
Vladimir Zelevinsky (Lansing, Michigan, USA)
E-Mail: Zelevins@nscl.msu.edu
WWW page: https://people.nscl.msu.edu/~zelevins/
Affiliation: Department of Physics and Astronomy and National Superconducting Cyclotron Laboratory Michigan State University, East Lansing, USA
Title: Atomic Nucleus as Chaotic Quantum Many-Body System
Abstract:
Complex atomic nuclei are quantum many-body systems with strong interaction between the constituents. With growing excitation energy, the combinatorics of fermionic levels makes the density of states extremely high, so that corresponding many-body wave functions become exceedngly complicated. At this stage the nuclei reveal typical properties of quantum chaos similar to the Gaussian Orthogonal Ensemble of random matrices. Based on the exact large-scale diagonalization of Hamiltonian matrices, we see these properties gradually arising as a function of excitation energy. This can be interpreted as thermalization in an isolated system where the interactions play the role of a heat bath. It will be shown how chaotic properties can be used as a practical tool for experiments, theory and computations. Finally, the applications to open systems with and without disorder will be discussed.
Karol Życzkowski (Warsaw, Poland)
E-Mail: karol@tatry.if.uj.edu.pl
WWW page: http://chaos.if.uj.edu.pl/~karol/
Affiliation: nstitute of Physics, Jagiellonian University, ul Łojasiewicza 11, 30-348 Cracow, Poland and Center for Theoretical Physics PAS, Al. Lotników 32/46, 02-668 Warsaw, Poland
Title: Quantum chaos in composite systems and properties of generic mixed quantum states
Abstract:
Unitary evolution operator of a quantum analogue of a classically chaotic system transforms a typical initial state into a delocalized random pure state. Analyzing such a unitary dynamics for a composite, bipartite system and performing partial trace over a selected subsystem one obtains a generic mixed state on the second subsystem. We investigate statistical properties of such generic mixed states and show that for a large dimension of the Hilbert space they become universal due to the effect of concentration of measure. In particular the trace distance between two random mixed states converges to 1/2+2/π, which due to the Helstom bound determines their discrimination in an optimal measurement scheme.
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