Stability of the vortex lattice in a rotating superfluid

TL;DR

This paper investigates the stability of vortex lattices in rotating superfluids, showing that considering three-dimensional modes ensures finite thermal displacements and lattice stability.

Contribution

It demonstrates that including the full three-dimensional spectrum of Tkachenko modes resolves the apparent instability caused by two-dimensional mode analysis.

Findings

Three-dimensional mode analysis yields finite thermal displacements.

Inclusion of 3D modes stabilizes the vortex lattice.

Two-dimensional analysis alone suggests instability.

Abstract

We analyze the stability of the vortex lattice in a rotating superfluid against thermal fluctuations associated with the long-wavelength Tkachenko modes of the lattice. Inclusion of only the two-dimensional modes leads formally to instability in infinite lattices; however, when the full three-dimensional spectrum of modes is taken into account, the thermally-induced lattice displacements are indeed finite.