Relaxation process in a regime of quantum chaos

TL;DR

This paper investigates the quantum relaxation process in classically chaotic open systems, revealing a characteristic quantum relaxation time scale that bridges classical and quantum decay behaviors.

Contribution

It introduces a quantum relaxation time scale t_q in chaotic systems, showing it is shorter than the Heisenberg time but longer than the Ehrenfest time, with a specific dependence on conductance.

Findings

Quantum relaxation time t_q scales as g^alpha with alpha close to 1/2.

Quantum and classical decay probabilities stay close up to P ~ exp(-sqrt(g)).

The relaxation process exhibits a distinct regime characterized by the scale t_q.

Abstract

We show that the quantum relaxation process in a classically chaotic open dynamical system is characterized by a quantum relaxation time scale t_q. This scale is much shorter than the Heisenberg time and much larger than the Ehrenfest time: t_q ~ g^alpha where g is the conductance of the system and the exponent alpha is close to 1/2. As a result, quantum and classical decay probabilities remain close up to values P ~ exp(-sqrt(g)) similarly to the case of open disordered systems.