Thermodynamic origin of the Landau instability of superfluids

TL;DR

This paper offers a unified thermodynamic framework explaining the Landau instability in superfluids, connecting classical and relativistic cases, and demonstrating its validity through gauge/gravity duality models.

Contribution

It introduces a thermodynamic criterion for superfluid instability that applies broadly, including dissipative and relativistic regimes, unifying previous understandings.

Findings

Instability onset corresponds to a sign change in the free energy second derivative matrix.

Dissipation induces a linear dynamical instability with exponential growth of perturbations.

The criterion matches Landau's critical velocity and applies to relativistic superfluids via gauge/gravity duality.

Abstract

In this work, we revisit the question of the linear stability of superfluid phases of matter. Famously, Landau predicted superfluid Helium would become unstable for large enough superfluid velocities. We demonstrate that this instability simply follows from a thermodynamic argument, by showing that its onset corresponds to a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Turning on dissipation and without any particular assumption on invariance under boosts, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of quasiparticles, our criterion matches Landau's critical velocity. We also verify that it correctly reproduces the onset of the instability in relativistic superfluids constructed using gauge/gravity duality. Our work provides a simple, comprehensive and unified description of the Landau instability for superfluids independently of the microscopic details of the system.