Entropy production and equilibration in Yang-Mills quantum mechanics

TL;DR

This paper introduces a systematic method to solve the Husimi equation of motion for quantum systems, demonstrating entropy saturation in 2D Yang-Mills quantum mechanics, linking coarse grained entropy to microcanonical entropy.

Contribution

It develops a general approach to solve the Husimi equation and constructs a conserved coarse grained Hamiltonian, applied to Yang-Mills quantum mechanics.

Findings

Coarse grained entropy saturates to microcanonical entropy.

Method provides a systematic way to track entropy growth.

Application to 2D Yang-Mills demonstrates entropy equilibration.

Abstract

The Husimi distribution provides for a coarse grained representation of the phase space distribution of a quantum system, which may be used to track the growth of entropy of the system. We present a general and systematic method of solving the Husimi equation of motion for an isolated quantum system, and we construct a coarse grained Hamiltonian whose expectation value is exactly conserved. As an application, we numerically solve the Husimi equation of motion for two-dimensional Yang-Mills quantum mechanics (the x-y model) and calculate the time evolution of the coarse grained entropy of a highly excited state. We show that the coarse grained entropy saturates to a value that coincides with the microcanonical entropy corresponding to the energy of the system.