Quantum-to-classical correspondence in open chaotic systems

TL;DR

This paper reviews how open chaotic mesoscopic systems transition from quantum to classical behavior as the Ehrenfest time increases, revealing deviations from universality predicted by random-matrix theory.

Contribution

It analyzes the impact of finite Ehrenfest time on quantum-to-classical correspondence and identifies resulting deviations from universal behavior in various physical phenomena.

Findings

Increasing Ehrenfest time leads to more deterministic transport modes.

Deviations from random-matrix universality become significant with larger Ehrenfest times.

The study covers effects on shot noise, conductance fluctuations, and quasibound state decay.

Abstract

We review properties of open chaotic mesoscopic systems with a finite Ehrenfest time tau_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, tau_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 quasibound states, and the mesoscopic proximity effect in Andreev billiards.