Energy spectra and fluxes of two-dimensional turbulent quantum droplets

TL;DR

This paper investigates the energy spectra and fluxes in turbulent two-dimensional quantum droplets under rotation, revealing various vortex configurations and scaling laws that deepen understanding of quantum turbulence and nonequilibrium dynamics.

Contribution

It provides a systematic analysis of turbulence regimes in quantum droplets, identifying specific spectral scalings and vortex behaviors influenced by external potentials and atom number.

Findings

Incompressible energy spectrum shows Kolmogorov and Vinen-like scaling.

Ultraviolet spectrum exhibits a $k^{-3}$ decay indicating vortices.

Energy cascade from large to small scales is observed through flux analysis.

Abstract

We explore the energy spectra and associated fluxes of turbulent two-dimensional quantum droplets subjected to a rotating paddling potential which is removed after a few oscillation periods. A systematic analysis on the impact of the characteristics (height and velocity) of the rotating potential and the droplet atom number reveals the emergence of different dynamical response regimes. These are classified by utilizing the second-order sign correlation function and the ratio of incompressible versus compressible kinetic energies. They involve, vortex configurations ranging from vortex dipoles to vortex clusters and randomly distributed vortex-antivortex pairs. The incompressible kinetic energy spectrum features Kolmogorov ($k^{-5/3}$) and Vinen like ($k^{-1}$) scaling in the infrared regime, while a $k^{-3}$ decay in the ultraviolet captures the presence of vortices. The compressible spectrum shows $k^{-3/2}$ scaling within the infrared and $k$ power law in the case of enhanced sound-wave emission suggesting thermalization. Significant distortions are observed in the droplet periphery in the presence of a harmonic trap. A direct energy cascade (from large to small length scales) is mainly identified through the flux. Our findings offer insights into the turbulent response of exotic phases-of-matter, featuring quantum fluctuations, and may inspire investigations aiming to unravel self-similar nonequilibrium dynamics.