Strong and weak wave turbulence regimes in Bose-Einstein condensates

TL;DR

This study numerically investigates wave turbulence in a 3D Bose-Einstein condensate, revealing a transition from weak-wave cascade to a critical balance state and eventually to a coherent condensate with acoustic turbulence as forcing increases.

Contribution

It introduces a detailed numerical analysis of turbulence regimes in BECs, identifying a transition from weak to critical balance and coherent states under varying forcing conditions.

Findings

Turbulence spectrum transitions from weak-wave cascade to critical balance with increased forcing.

A new out-of-equilibrium equation of state for the 3D inverse cascade is formulated.

Vortices play a marginal role in the strongly forced turbulent state.

Abstract

When a turbulent Bose-Einstein condensate is driven out-of-equilibrium at a scale much smaller than the system size, nonlinear wave interactions transfer particles towards large scales in an inverse cascade process. In this work, we study numerically wave turbulence in a three-dimensional Bose-Einstein condensate in forced and dissipated inverse cascade settings. We observe that when the forcing rate increases, thereby increasing the particle flux, the turbulence spectrum gradually transitions from the weak-wave Kolmogorov-Zakharov cascade to a critical balance state characterized by a range of scales with balanced linear and nonlinear dynamic timescales. Further forcing increases lead to a coherent condensate component superimposed with Bogoliubov-type acoustic turbulence. The role of vortices in such a strongly forced state is marginal, which makes this new state very different from the strongly turbulent state composed of a tangle of quantized vortex lines. We then use our predictions and numerical data to formulate a new out-of-equilibrium equation of state for the 3D inverse cascade.