# Decaying quantum turbulence in a two-dimensional Bose-Einstein condensate at finite temperature

## TL;DR

This study models how quantum turbulence in a 2D Bose-Einstein condensate decays at finite temperatures, revealing temperature-dependent vortex behaviors and fixed points.

## Contribution

It introduces a numerical approach to analyze finite-temperature effects on 2D quantum turbulence, highlighting vortex dynamics and fixed point transitions.

## Key findings

- At low temperatures, vortex clustering occurs with negative vortex temperature.
- At higher temperatures, vortex dipoles dominate, leading to positive vortex temperature.
- The system evolves toward either a non-thermal or thermal fixed point depending on temperature.

## Abstract

We numerically model decaying quantum turbulence in two-dimensional disk-shaped Bose-Einstein condensates, and investigate the effects of finite temperature on the turbulent dynamics. We prepare initial states with a range of condensate temperatures, and imprint equal numbers of vortices and antivortices at randomly chosen positions throughout the fluid. The initial states are then subjected to unitary time-evolution within the c-field methodology. For the lowest condensate temperatures, the results of the zero temperature Gross-Pitaevskii theory are reproduced, whereby vortex evaporative heating leads to the formation of Onsager vortex clusters characterised by a negative absolute vortex temperature. At higher condensate temperatures the dissipative effects due to vortex-phonon interactions tend to drive the vortex gas towards positive vortex temperatures dominated by the presence of vortex dipoles. We associate these two behaviours with the system evolving toward an anomalous non-thermal fixed point, or a Gaussian thermal fixed point, respectively.