Vortex Formation in Two-Dimensional Bose Gas

TL;DR

This paper investigates the stability of a two-dimensional Bose gas at finite temperature, revealing an instability linked to vortex formation that may correspond to the BKT transition, using Euclidean formalism and dilute gas approximation.

Contribution

It introduces a novel analysis of vortex-related instabilities in 2D Bose gases at finite temperature using symmetry-breaking formalism and Euclidean methods.

Findings

Identification of vortex-induced free energy imaginary part

Demonstration of instability associated with BKT transition

Application of dilute gas approximation to vortex configurations

Abstract

We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated to isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii, Kosterlitz and Thouless (BKT) transition.