Direct and inverse cascades in turbulent Bose-Einstein condensate

TL;DR

This paper analytically and numerically investigates the energy and particle cascades in turbulent Bose-Einstein condensates, deriving spectra and validating predictions with simulations and experimental relevance.

Contribution

It provides the first analytical derivation of Kolmogorov-Zakharov spectra for turbulent BECs, including log-corrections and universal constants, validated by high-resolution simulations.

Findings

Analytical spectra match numerical simulations.

Validated predictions with experimental configurations.

Confirmed inverse and direct cascade behaviors in BEC turbulence.

Abstract

When a Bose-Einstein condensate (BEC) is driven out of equilibrium, density waves interact non-linearly and trigger turbulent cascades. In a turbulent BEC, energy is transferred towards small scales by a direct cascade, whereas the number of particles displays an inverse cascade toward large scales. In this work, we study analytically and numerically the direct and inverse cascades in wave-turbulent BECs. We analytically derive the Kolmogorov-Zakharov spectra, including the log-correction to the direct cascade scaling and the universal pre-factor constants for both cascades. We test and corroborate our predictions using high-resolution numerical simulations of the forced-dissipated Gross-Pitaevskii model in a periodic box and the corresponding wave-kinetic equation. Theoretical predictions and data are in excellent agreement, without adjustable parameters. Moreover, in order to connect with experiments, we test and validate our theoretical predictions using the Gross-Pitaevskii model with a confining cubic trap. Our results explain previous experimental observations and suggest new settings for future studies.