Quantum relaxation in open chaotic systems

TL;DR

This paper analytically derives how quantum relaxation in open chaotic systems follows classical decay up to a new, larger quantum time scale using supersymmetry techniques, revealing symmetry-dependent decay behaviors.

Contribution

It provides an analytical derivation of the quantum relaxation time scale in open chaotic systems, extending previous numerical results with supersymmetry methods.

Findings

Quantum decay follows classical decay up to time scale t_q

Quantum relaxation time scale t_q ~ sqrt(t_c t_H)

Decay behavior varies with symmetry class (orthogonal, unitary, symplectic)

Abstract

Using the supersymmetry technique, we analytically derive the recent result of Casati, Maspero and Shepelyansky [cond-mat/9706103] according to which the quantum dynamics of open chaotic systems follows the classical decay up to a new quantum relaxation time scale $t_q\sim\sqrt{t_c t_H}$. This scale is larger than the classical escape time $t_c$ but still much smaller than the Heisenberg time $t_H$. For systems with orthogonal or unitary symmetry the quantum decay is slower than the classical one while for the symplectic case there is an intermediate regime in which the quantum decay is slightly faster.