# Decay of a quantum vortex: test of non-equilibrium theories for warm Bose-Einstein condensates

## TL;DR

This paper models vortex decay in high-temperature Bose-Einstein condensates using the stochastic projected Gross-Pitaevskii equation, providing detailed lifetime predictions and testing non-equilibrium theories.

## Contribution

It introduces a Hartree-Fock method to estimate SPGPE parameters and compares vortex decay predictions across three classical field theories, highlighting SPGPE's superior accuracy.

## Key findings

- Vortex lifetime decreases linearly with temperature.
- SPGPE predicts shorter vortex lifetimes than other theories.
- Calculated vortex lifetime ranges from 1.5 to 20 seconds.

## Abstract

The decay of a vortex from a non-rotating high temperature Bose-Einstein condensate (BEC) is modeled using the stochastic projected Gross-Pitaevskii equation (SPGPE). In order to exploit the tunability of temperature in SPGPE theory while maintaining the total atom number constant, we develop a simple and accurate Hartree-Fock method to estimate the SPGPE parameters for systems close to thermal equilibrium. We then calculate the lifetime of a vortex using three classical field theories that describe vortex decay in different levels of approximation. The SPGPE theory is shown to give the most complete description of the decay process, predicting significantly shorter vortex lifetimes than the alternative theories. Using the SPGPE theory to simulate vortex decay for a trapped gas of $5\times 10^5$ $^{87}$Rb atoms, we calculate a vortex lifetime $\bar{t}$ that decreases linearly with temperature, falling in the range 20{\rm s}$ >\bar{t} >$1.5{\rm s} corresponding to the temperature range $0.78T_c\leq T\leq0.93T_c$. The vortex lifetimes calculated provide a lower bound for the lifetime of a persistent current with unit winding number in our chosen trap geometry, in the limit of vanishing vortex pinning potential.