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.
Highlights
We imprint vortices on these microstates to form an ensemble of vortex distributions, and determine the resulting effect of the finite temperature on the turbulent vortex dynamics by integrating the microcanoncial projected Gross–Pitaevskii equation (PGPE) that conserves both energy and normalisation of the classical field
In this work we model the dynamics of a partially-condensed Bose gas at finite temperature using a projected [32, 33, 37] and stochastic projected [33, 34, 38] Gross–Pitaevskii equation
In order to determine whether the system is undergoing universal dynamics, we look for selfsimilar evolution in the statistical properties of the field ψ(r), as predicted by the dynamical scaling hypothesis [58]
Summary
Developing a complete understanding of turbulent dynamics in fluids remains a significant challenge in contemporary physics. The same authors found that the inclusion of phenomenological dissipation representing the effects of damping due to finite condensate temperature had a deleterious effect on the formation of Onsager vortices [22] These findings raised important questions regarding the possibility of experimentally observing Onsager vortices in decaying two-dimensional quantum turbulence, and motivate more quantitative studies of the effect of the temperature of the atoms in these systems. Rather than incorporating thermal atom effects in the Gross–Pitaevskii equation (GPE) using a phenomenological damping term, we instead perform dynamical simulations using the classical field methodology [31,32,33]. We imprint vortices on these microstates to form an ensemble of vortex distributions, and determine the resulting effect of the finite temperature on the turbulent vortex dynamics by integrating the microcanoncial projected Gross–Pitaevskii equation (PGPE) that conserves both energy and normalisation of the classical field.
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