Counterflow instability and turbulence in a spin-1 spinor Bose--Einstein condensate

TL;DR

This paper investigates counterflow-induced turbulence in spin-1 Bose--Einstein condensates, revealing how ferromagnetic and antiferromagnetic interactions influence turbulence spectra and dynamics.

Contribution

It provides a theoretical analysis of turbulence in spinor BECs, highlighting the impact of spin-dependent interactions on turbulence spectra and behavior.

Findings

Ferromagnetic case shows a -7/3 power law in energy spectrum.

Antiferromagnetic case does not exhibit the -7/3 power law.

Scaling analysis explains the -7/3 power law in the ferromagnetic case.

Abstract

We theoretically study counterflow instability and turbulence in a spin-1 spinor Bose--Einstein condensate by the Gross--Pitaevskii equation and the Bogoliubov--de Gennes equation. Our study considers (i) the dynamics induced by the counterflow of two components with different magnetic quantum numbers, which leads to turbulence with spin degrees of freedom, and (ii) the properties of the turbulence. For (i), the behavior of the condensate induced by the counterflow strongly depends on whether the spin-dependent interaction is ferromagnetic or antiferromagnetic, leading to different behaviors for the dispersion relation and the spin density vector, $etc$. For (ii), we numerically calculate the spectrum of the spin-dependent interaction energy, which also depends on the spin-dependent interaction. The spectrum of the spin-dependent interaction energy in the ferromagnetic case exhibits a -7/3 power law, whereas that in the antiferromagnetic case does not. The -7/3 power law can be explained by scaling analysis.