A semi-classical field method for the equilibrium Bose gas and application to thermal vortices in two dimensions

TL;DR

This paper introduces a semi-classical field method for the equilibrium Bose gas that avoids ultraviolet cut-off issues and applies it to analyze thermal vortices in two-dimensional systems, providing numerical and analytical insights.

Contribution

A novel semi-classical field method for the weakly interacting Bose gas that eliminates ultraviolet cut-off dependence and enables detailed vortex analysis.

Findings

Vortex density and pair distribution functions computed

Activation energy for vortex pair formation determined

Comparison with analytical models enhances understanding

Abstract

We develop a semi-classical field method for the study of the weakly interacting Bose gas at finite temperature, which, contrarily to the usual classical field model, does not suffer from an ultraviolet cut-off dependence. We apply the method to the study of thermal vortices in spatially homogeneous, two-dimensional systems. We present numerical results for the vortex density and the vortex pair distribution function. Insight in the physics of the system is obtained by comparing the numerical results with the predictions of simple analytical models. In particular, we calculate the activation energy required to form a vortex pair at low temperature.