Berlin 2012 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 23: Quantum Chaos I
DY 23.4: Talk
Thursday, March 29, 2012, 10:15–10:30, MA 001
Fractal Weyl Law in Systems with a Mixed Phase Space? — Arnd Bäcker1,2, Roland Ketzmerick1,2, •Martin Körber1, and Matthias Michler1 — 1Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany — 2MPI für Physik komplexer Systeme, 01187 Dresden, Germany
A characteristic feature of open systems is the escape of classical orbits and the decay of quantum states. In ergodic systems the number of long-lived states obeys a fractal Weyl law, where the exponent is associated to the fractal dimension of the repeller. In generic Hamiltonian systems with a mixed phase space, where regular and chaotic motion coexist, the structure of the repeller and its quantum implications are open questions.
In such systems the transport in the chaotic sea is governed by the hierarchy of partial barriers. We design a controllable model system which captures this property. Classically, we analyze the impact on the repeller. Quantum mechanically, we investigate the interplay between the location of eigenstates in the hierarchy and their decay rates in order to clarify the impact on the fractal Weyl law.