Calculation of the microcanonical temperature for the classical Bose field

TL;DR

This paper details a method to calculate temperature and chemical potential from the dynamics of a microcanonical classical Bose field, aiding in understanding non-perturbative effects on Bose gas critical temperature.

Contribution

It introduces a precise approach to determine thermodynamic quantities from classical field dynamics, specifically applied to Bose-condensed gases.

Findings

Method enables accurate temperature measurement from classical field dynamics

Facilitates study of non-perturbative effects on Bose gas critical temperature

Enhances understanding of ergodic properties in classical Bose systems

Abstract

The ergodic hypothesis asserts that a classical mechanical system will in time visit every available configuration in phase space. Thus, for an ergodic system, an ensemble average of a thermodynamic quantity can equally well be calculated by a time average over a sufficiently long period of dynamical evolution. In this paper we describe in detail how to calculate the temperature and chemical potential from the dynamics of a microcanonical classical field, using the particular example of the classical modes of a Bose-condensed gas. The accurate determination of these thermodynamics quantities is essential in measuring the shift of the critical temperature of a Bose gas due to non-perturbative many-body effects.