Occurrence of exponential relaxation in closed quantum systems

TL;DR

This paper explores the conditions under which exponential relaxation occurs in closed quantum systems, emphasizing the importance of perturbation structure and timescale separation, supported by numerical simulations.

Contribution

It identifies specific criteria, including the Van Hove structure, necessary for exponential relaxation in closed quantum systems, extending understanding of relaxation dynamics.

Findings

Exponential relaxation depends on perturbation strength and structure.

Higher-order effects can disrupt exponential behavior.

Numerical simulations confirm theoretical predictions.

Abstract

We investigate the occurrence of exponential relaxation in a certain class of closed, finite systems on the basis of a time-convolutionless (TCL) projection operator expansion for a specific class of initial states with vanishing inhomogeneity. It turns out that exponential behavior is to be expected only if the leading order predicts the standard separation of timescales and if, furthermore, all higher orders remain negligible for the full relaxation time. The latter, however, is shown to depend not only on the perturbation (interaction) strength, but also crucially on the structure of the perturbation matrix. It is shown that perturbations yielding exponential relaxation have to fulfill certain criteria, one of which relates to the so-called ``Van Hove structure''. All our results are verified by the numerical integration of the full time-dependent Schroedinger equation.