Finite-temperature dynamics of a single vortex in a Bose-Einstein condensate: Equilibrium precession and rotational symmetry breaking

TL;DR

This paper investigates the equilibrium behavior and symmetry breaking of a single vortex in a finite-temperature Bose-Einstein condensate, revealing how off-axis vortices emerge and how symmetry is broken in classical-field models.

Contribution

It introduces a methodology to identify the condensate and Goldstone mode in a classical-field model, and analyzes vortex dynamics and symmetry breaking at finite temperature.

Findings

Vortex configurations arise as ergodic equilibrium states constrained by angular momentum.

Rotational symmetry is broken by off-axis vortex condensation in isotropic traps.

Vortex trajectories and thermodynamic parameters vary with energy in microcanonical simulations.

Abstract

We consider a finite-temperature Bose-Einstein condensate in a quasi-two-dimensional trap containing a single precessing vortex. We find that such a configuration arises naturally as an ergodic equilibrium of the projected Gross-Pitaevskii equation, when constrained to a finite conserved angular momentum. In an isotropic trapping potential the condensation of the classical field into an off-axis vortex state breaks the rotational symmetry of the system. We present a methodology to identify the condensate and the Goldstone mode associated with the broken rotational symmetry in the classical-field model. We also examine the variation in vortex trajectories and thermodynamic parameters of the field as the energy of the microcanonical field simulation is varied.