Perturbative Approach to Superfluidity under Nonuniform Potential

TL;DR

This paper introduces a perturbative method to analyze superfluidity in systems with nonuniform potentials, applicable across various quantum systems without assuming Bose-Einstein condensation, and explores several specific models.

Contribution

It develops a general perturbation expansion for the superfluid fraction that relates to density fluctuations, applicable to diverse quantum systems without relying on Bose-Einstein condensation assumptions.

Findings

Derived the perturbation expansion of superfluid fraction.

Applied the formulation to multiple quantum systems.

Identified the role of density fluctuations in superfluid behavior.

Abstract

A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose systems, especially Bose gas in the mean field limit, (non-)interacting Fermi sytems, Tomonaga-Luttinger liquid and spinless chiral $p$-wave superfluid are investigated.