Relativistic superfluid profiles near critical surfaces

TL;DR

This paper develops a relativistic framework for superfluid profiles near critical surfaces, analyzing stability, critical velocities, and phase boundary phenomena, extending classical models into relativistic regimes.

Contribution

It introduces a relativistic Gross-Pitaevskii-type model to study superfluid behavior near phase boundaries, providing exact expressions and stability analysis.

Findings

Standard superfluid profiles remain valid in relativistic settings.

Derived an exact formula for Landau's critical velocity.

Identified relativistic effects on phase boundary formation.

Abstract

Landau's two-fluid model of superfluidity ceases to apply in regions where the condensate amplitude exhibits rapid spatial variation, such as vortex cores or in the vicinity of container walls. A recently proposed relativistic Gross-Pitaevskii-type framework treats the condensate as an independent scalar degree of freedom, enabling a controlled analysis of such regimes. We use it to construct stationary superflows close to the superfluid-normal phase boundary, and examine their stability. We obtain an exact expression for Landau's critical velocity and show that the standard Newtonian profiles (such as the near-vortex condensate depletion or the boundary-layer decay) persist unmodified in the relativistic setting. We further analyse a genuinely relativistic configuration in which an accelerated superfluid develops a phase boundary induced by Tolman temperature gradients.