Plenarvorträge - DPG-Tagungen

Dynamik und Statistische Physik Dienstag
DY 27 Quantum Chaos
Zeit: Dienstag 16:30–18:15 Raum: H3
DY 27.1 Di 16:30 H3
Microwave measurements on dielectric quadrupole billards —
•R. Schäfer and H.-J. Stöckmann — Fachbereich Physik, Philipps-
Universität Marburg, Renthof 5, D-35032 Marburg, Germany
Quadrupole dielectic billiards have received a lot of attention because
of their highly directed emission patterns [1] which is a welcome effect in
the design of microdisc lasers. We measured transmission spectra from a
fixed antenna inside the disc to a moveable antenna, thus scanning both
the inside and outside region of the teflon disc. A Fourier transform of
the spectra yields the pulse propagation. The long time behavior is dominated
by the whispering gallery modes, which decay very slowly due to
total internal reflection. The emission pattern of the quadrupole billiard
is strongly influenced by the structures of its mixed phase space. Even for
strong deformations with no stable islands left, a high directionality of
the emission is found. This can be explained by the unstable manifolds of
periodic orbits [2]. The internal dynamics of the pulse has been analyzed
by means of Husimi distributions, while for the outer region the Poynting
vector was calculated to obtain the emission pattern. Both are compared
with classical ray dynamics taking into account the curvature-corrected
Fresnel formula.
[1] J.U. Nöckel, A.D. Stone, Nature 385, 45 (1997)
[2] H.G.L Schwefel et al., arXiv:physics/0308001
DY 27.2 Di 16:45 H3
Quantum Chaos on Networks — •Holger Schanz — Max-Planck
Institut für Strömungsforschung und Institut für Nichtlineare Dynamik
der Universität Göttingen, Bunsenstr. 10, 37073 Göttingen
Quantized networks are simple models which allow to study quantum
signatures of classical chaos. They allow analytical approaches to unsolved
problems in quantum chaos, including periodic-orbit theories for
spectral correlations, transport and localization phenomena as well as
scarring of wavefunctions. A brief account of the model and the obtained
results will be given.
H. Schanz and U. Smilansky, Phys. Rev. Lett. 84(00)1427.
G. Berkolaiko, H. Schanz, R. S. Whitney, Phys. Rev. Lett. 88(02)104101.
H. Schanz and T. Kottos, Phys. Rev. Lett. 90(03)234101.
H. Schanz, M. Puhlmann and T. Geisel, Phys. Rev. Lett. 91(03)134101.
DY 27.3 Di 17:00 H3
Ray-wave correspondence in a fully chaotic quasi-stadium laser
resonator — •J. Wiersig 1 , T. Fukushima 2 , and T. Harayama 3
— 1 Universität Bremen — 2 Okayama Prefectural University, Okayama,
Japan — 3 ATR Adaptive Communication Research Laboratories, Kyoto,
Japan
The relation between resonator modes and unstable periodic orbits in
a fully chaotic quasi-stadium laser resonator is investigated. The complicated
wavelength dependence of the power coupling coefficient is explained
by a simple coupling model, which considers some unstable periodic
orbits.
DY 27.4 Di 17:15 H3
Semiclassical approximations for open systems: transport and
decay — •Mathias Puhlmann, Holger Schanz, Tsampikos Kottos,
and Theo Geisel — Max-Planck Institut für Strömungsforschung
und Institut für Nichtlineare Dynamik der Universität Göttingen, Bunsenstr.
10, 37073 Göttingen
DY 28 Glasses I (joint session DF/DY)
Important and diverse physical applications like electronic transport
through mesoscopic devices or microcrystal lasers require an understanding
of open quantum systems with chaotic classical limit. For many interesting
processes in such systems the interference between classical trajectories
is decisive. Therefore the standard semiclassical theory based on
the diagonal approximation is not accurate or fails at all. Using quantum
graphs as model systems we show how one can improve the semiclassical
description such that shot noise and the short-time devitions from a
simple exponential probability decay are reproduced.
H. Schanz, M. Puhlmann and T. Geisel, Phys. Rev. Lett. 91(03)134101.
DY 27.5 Di 17:30 H3
Semiclassical approach to shot noise in chaotic systems —
•Andreas Lassl, Marko Turek, and Klaus Richter — Institut
für Theoretische Physik, Universität Regensburg, D-93040 Regensburg
We propose a semiclassical approach to shot noise in clean chaotic
systems [1]. Starting from the semiclassical expression for the transmission
we derive the Fano factor in terms of classical paths. As expected
the application of the diagonal approximation yields a vanishing result
for the Fano factor. Therefore one has to include action correlations between
classical paths which can be expressed in terms of a crossing angle
distribution as in [2]. Here we present detailed numerical studies of this
crossing angle distribution in open systems.
[1] C.W.J. Beenakker and C. Schönenberger, Physics Today, 56 (5), 37-
42 (2003)
[2] K. Richter and M. Sieber, PRL 89, 206801 (2002)
DY 27.6 Di 17:45 H3
Universal spectral form factor for chaotic dynamics I: The
Hadamard-Gutzwiller model — Stefan Heusler, •Sebastian
Müller, Petr Braun, and Fritz Haake — Fachbereich Physik, Universität
Duisburg-Essen, 45117 Essen
We consider the semiclassical limit of the spectral form factor K(τ) of
the Hadamard-Gutzwiller model. Starting from the Gutzwiller type double
sum over classical periodic orbits we set out to recover the universal
behavior predicted by random-matrix theory, both for dynamics with and
without time reversal invariance. For times smaller than half the Heisenberg
time TH ∝ ¯h −f+1 , we extend the previously known τ-expansion to
include the cubic term. Our results exemplify the “diagrammatic rules”
determining the families of orbit pairs responsible for all orders of the
τ-expansion.
DY 27.7 Di 18:00 H3
Universal spectral form factor for chaotic dynamics II: General
systems — •Stefan Heusler, Sebastian Müller, Petr Braun
und Fritz Haake — Fachbereich Physik, Universität Duisburg-Essen,
45117 Essen
We consider the semiclassical limit of the spectral form factor K(τ)
of general, fully hyperbolic dynamics. Generalizing results for the
Hadamard-Gutzwiller model, we discuss the families of orbit pairs giving
rise to higher-order contributions to the spectral form factor.
Zeit: Dienstag 09:30–12:30 Raum: H23
Hauptvortrag DY 28.1 Di 09:30 H23
Theory of the glass transition for systems with trivial statics —
•Rolf Schilling 1 and Grzegorz Szamel 2 — 1 Institut für Physik,
Johannes Gutenberg-Universität, D-55099 Mainz — 2 Department of
Chemistry, Colorado State University, Ft. Collins, CO 80523, USA
The mode coupling theory (MCT) derived and investigated in great
detail by Götze and his coworkers has been the most important step to-
wards the microscopic understanding of the structural glass transition.
MCT yields a glass transition if the static correlations reach a critical
value. However, there exist systems with trivial statics where static correlations
even vanish. Nevertheless they exhibit a discontinuous glass
transition which can not be described by MCT in its present form. In
a first step we have derived a self-consistent equation for the diffusion
constant which yields a continuous transition, in contrast to simulational