From Classical Fields to Two-Fluid Model of Superfluidity: Emergent Kinetics and Local Gauge Transformations

TL;DR

This paper derives a two-fluid model of superfluidity from classical field theory using local gauge transformations, providing a more general framework that extends Landau's phenomenological approach.

Contribution

It introduces a novel derivation of the two-fluid model from classical fields via local gauge transformations, avoiding small parameter assumptions.

Findings

Kinetic equations resemble C12 and C22 collision terms.

Two-fluid model derivation from classical fields without small parameters.

Potential broader applicability beyond scale separation assumptions.

Abstract

The first successful macroscopic theory for the motion of superfluid helium was that of Lev Landau (1941) in which the fluid is modelled phenomenologically as an interpenetrating mixture of a superfluid and a normal fluid. It has later been shown that Landau's two-fluid model can be rigorously derived from a one-fluid model within the classical fields approximation. Assuming a separation of scales exists between the slowly varying, large-scale, background (condensate) field, and the short rapidly evolving excitations, a full description of the kinetics between the condensate and the thermal cloud can be obtained. The kinetics describes three-wave and four-wave interactions that resemble the C_{12} and C_{22} terms, respectively, in the collision integral of the ZNG theory. The scale separation assumption precludes analysis of the healing layer and thus does not include the dynamics of quantised vortices. Whilst the analysis required the use of small parameters arising from the scale separation assumption and the assumption of a weakly depleted condensate, we expect the results to hold true over a wider range of parameters. This belief is motivated by the validity of Landau's two-fluid model which can be derived from a one-fluid model using nothing more than Galilean invariance principles. Indeed, we argue that similar arguments can be used to recover a two-fluid model directly from a classical field simply by invoking a local gauge transformation. This derivation does not require any small parameters to be introduced suggesting that the results that lead to the kinetic equations may turn out to be more general.