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Quantum-to-classical correspondence in open chaotic systems.

Research output: Contribution to journalJournal articlepeer-review

Published
<mark>Journal publication date</mark>9/12/2005
<mark>Journal</mark>Journal of Physics A: Mathematical and General
Issue number49
Volume38
Number of pages20
Pages (from-to)10663-10682
Publication StatusPublished
<mark>Original language</mark>English

Abstract

We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time �E. The Ehrenfest time separates a short-time regime of the quantum dynamics, where wave packets closely follow the deterministic classical motion, from a long-time regime of fully-developed wave chaos. For a vanishing Ehrenfest time the quantum systems display a degree of universality which is well described by random-matrix theory. In the semiclassical limit, �E becomes parametrically larger than the scattering time off the boundaries and the dwell time in the system. This results in the emergence of an increasing number of deterministic transport and escape modes, which induce strong deviations from random-matrix universality. We discuss these deviations for a variety of physical phenomena, including shot noise, conductance fluctuations, decay of quasi-bound states and the mesoscopic proximity effect in Andreev billiards.