Entropy production in quantum Yang-Mills mechanics in semi-classical approximation

TL;DR

This paper investigates entropy production in quantum systems using semiclassical approximations of Husimi-Wehrl entropy, demonstrating efficient methods for numerical evaluation in chaotic quantum systems.

Contribution

It introduces two novel numerical methods for evaluating Husimi-Wehrl entropy evolution in semiclassical quantum systems, validating their reliability.

Findings

Semiclassical approximation effectively describes entropy production in chaotic quantum systems.

Two numerical methods, test-particle and two-step Monte Carlo, produce consistent results.

The methods are demonstrated to be efficient and reliable through numerical tests.

Abstract

We discuss thermalization of isolated quantum systems by using the Husimi-Wehrl entropy evaluated in the semiclassical treatment. The Husimi-Wehrl entropy is the Wehrl entropy obtained by using the Husimi function for the phase space distribution. The time evolution of the Husimi function is given by smearing the Wigner function, whose time evolution is obtained in the semiclassical approximation. We show the efficiency and usefullness of this semiclassical treatment in describing entropy production of a couple of quantum mechanical systems, whose classical counter systems are known to be chaotic. We propose two methods to evaluate the time evolution of the Husimi-Wehrl entropy, the test-particle method and the two-step Monte-Carlo method. We demonstrate the characteristics of the two methods by numerical calculations, and show that the simultaneous application of the two methods ensures the reliability of the results of the Husimi-Wehrl entropy at a given time.