Non-equilibrium Bose-Einstein Condensation

TL;DR

This paper explores non-equilibrium Bose-Einstein condensation through numerical simulations, comparing turbulent spectrum evolution with wave turbulence theory, and identifying regimes of weak and strong turbulence.

Contribution

It demonstrates the agreement between numerical simulations and wave turbulence theory for non-equilibrium BEC formation, including power-law spectra and turbulence regimes.

Findings

Good agreement with wave turbulence results in certain regimes

Identification of anomalous power-law exponent in wave-action spectrum

Observation of vortex formation in strong turbulence regime

Abstract

We investigate formation of Bose-Einstein condensates under non-equilibrium conditions using numerical simulations of the three-dimensional Gross-Pitaevskii equation. For this, we set initial random weakly nonlinear excitations and the forcing at high wave numbers, and study propagation of the turbulent spectrum toward the low wave numbers. Our primary goal is to compare the results for the evolving spectrum with the previous results obtained for the kinetic equation of weak wave turbulence. We demonstrate existence of a regime for which good agreement with the wave turbulence results is found in terms of the main features of the previously discussed self-similar solution. In particular, we find a reasonable agreement with the low-frequency and the high-frequency power-law asymptotics of the evolving solution, including the anomalous power-law exponent $x^* \approx 1.24$ for the three-dimensional waveaction spectrum. We also study the regimes of very weak turbulence, when the evolution is affected by the discreteness of the Fourier space, and the strong turbulence regime when emerging condensate modifies the wave dynamics and leads to formation of strongly nonlinear filamentary vortices.