Dynamic scaling of vorticity in phase-separating superfluid mixtures

TL;DR

This paper investigates the dynamic scaling law of vorticity structure factor in phase-separating superfluid mixtures, revealing a power-law energy spectrum hierarchy and proposing a decay law based on turbulence theory.

Contribution

It introduces a theoretical and numerical analysis of the vorticity structure factor's dynamic scaling law in binary superfluid mixtures, extending turbulence concepts to superfluid phase separation.

Findings

Identified a dynamic scaling law for the vorticity structure factor.

Discovered a power-law hierarchy in the energy spectrum.

Proposed a decay law of energy incorporating a high-wavenumber cutoff.

Abstract

Recently, it has been experimentally confirmed that non-equilibrium dynamics of phase separation in strongly ferromagnetic Bose-Einstein condensates of $^7$Li atoms obey the dynamic scaling law belonging to the binary-fluid universality class in the inertial hydrodynamic stage. The current work theoretically and numerically studies the dynamic scaling law of structure factor of vorticity in a phase-separating binary superfluid mixture, equivalent to the $^7$Li condensates in a strong limit of quadratic Zeeman shift. We found a dynamic scaling law for the structure factor based on our numerical observation that the peak of the energy spectrum from turbulence theory does not vary in time in the stage. Similarly to freely decaying turbulence, a power-law hierarchy exists in the energy spectrum in our system, and we proposed a decay law of the energy based on the dynamic scaling law by introducing the microscopic, high-wavenumber cutoff.