From inverse-cascade to sub-diffusive dynamic scaling in driven disordered Bose fluids

TL;DR

This paper investigates the universal dynamic scaling behavior in driven disordered Bose gases near condensation, revealing a crossover from inverse cascade to sub-diffusive regimes governed by self-similar laws.

Contribution

It introduces a comprehensive analysis of the crossover between different dynamical regimes in driven disordered Bose fluids, highlighting the emergence of self-similar scaling laws.

Findings

Identification of three distinct dynamical regimes in the Bose gas

Demonstration of self-similar scaling laws in all regimes

Observation of sub-diffusive energy cascade consistent with experiments

Abstract

We explore the emergence of universal dynamic scaling in an interacting Bose gas around the condensation transition, under the combined influence of an external driving force and spatial disorder. As time progresses, we find that the Bose gas crosses over three distinct dynamical regimes: (i) an inverse turbulent cascade where interactions dominate the drive, (ii) a stationary regime where the inverse cascade and the drive counterbalance one other, and (iii) a sub-diffusive cascade in energy space governed by the drive and disorder, a phenomenon recently observed experimentally. We show that all three dynamical regimes can be described by self-similar scaling laws.