Statistical Relaxation in Closed Quantum Systems and the Van Hove-Limit

TL;DR

This paper investigates how statistical relaxation occurs in closed quantum systems, showing that it depends on interaction structure and deriving conditions under which it emerges in the Van Hove-limit.

Contribution

It provides both numerical and analytical insights into the conditions for statistical dynamics in quantum systems, emphasizing the role of interaction structure.

Findings

Statistical dynamics depend on the interaction structure.

Numerical calculations illustrate the dependence.

Analytical derivation confirms statistical behavior in the Van Hove-limit.

Abstract

We analyze the dynamics of occupation probabilities for a certain type of design models by the use of two different methods. On the one hand we present some numerical calculations for two concrete interactions which point out that the occurrence of statistical dynamics depends on the interaction structure. Furthermore we show an analytical derivation for an infinite system that yields statistical behaviour for the average over the whole ensemble of interactions in the Van Hove-limit.