Thermal vortex dynamics in a two-dimensional condensate

TL;DR

This paper investigates the complex motion of a vortex in a two-dimensional condensate at thermal equilibrium, revealing non-Gaussian flight distributions and a dual interpretation as a massive particle and a passive scalar.

Contribution

It provides an analytical and numerical analysis of vortex dynamics including hydrodynamic fluctuations, highlighting non-Gaussian behavior and dual physical interpretations.

Findings

Vortex motion exhibits non-Gaussian exponential tails.

Vortex behaves as a massive particle in a heat bath.

Vortex also acts as a passive scalar in a random flow.

Abstract

We carry out an analytical and numerical study of the motion of an isolated vortex in thermal equilibrium, the vortex being defined as the point singularity of a complex scalar field $\psi(\r,t)$ obeying a nonlinear stochastic Schr\"odinger equation. Because hydrodynamic fluctuations are included in this description, the dynamical picture of the vortex emerges as that of both a massive particle in contact with a heat bath, and as a passive scalar advected to a background random flow. We show that the vortex does not execute a simple random walk and that the probability distribution of vortex flights has non-Gaussian (exponential) tails.