Dynamical Density Fluctuation of Superfluids near Critical Velocities

TL;DR

This paper introduces a new stability criterion for superfluids near critical velocities, based on density fluctuation spectral functions, validated through theoretical analysis of various instabilities.

Contribution

It presents a novel stability criterion for superfluids that incorporates spectral functions, validated within the Gross-Pitaevskii-Bogoliubov framework for multiple instability types.

Findings

Validates the criterion for soliton-emission instability

Applicable to Landau phonon and roton instabilities

Uses explicit zero modes and dynamical scaling analysis

Abstract

We propose a stability criterion of superfluids in condensed Bose-Einstein systems, which incorporates the spectral function or the autocorrelation function of the local density. Within the Gross-Pitaevskii-Bogoliubov theory, we demonstrate the validity of our criterion for the soliton-emission instability, with use of explicit forms of zero modes of the Bogoliubov equation and a dynamical scaling near the saddle-node bifurcation. We also show that the criterion is applicable to the Landau phonon instability and the Landau roton instability within the single-mode approximation.