Low energy dynamics of gapless and quasi-gapless modes of vortices in superfluid $^3$He-B

TL;DR

This paper analyzes the low energy excitations of vortices in superfluid helium-3 B phase, deriving an effective theory for their gapless modes based on symmetry considerations and vortex solutions.

Contribution

It provides a detailed derivation of the low energy effective dynamics of vortex excitations in superfluid helium-3 B phase, including stability conditions and symmetry-breaking analysis.

Findings

Derived vortex solutions using an ansatz for the order parameter.

Calculated stability conditions for vortex solutions.

Formulated the effective free energy for vortex excitations.

Abstract

We discuss the low energy effective dynamics of gapless excitations of the mass vortices of systems similar to the Ginzburg-Landau description of superfluid helium-3 in the bulk B phase. Our approach is to determine the vortex solution by considering a specific ansatz for the order parameter and minimizing the free energy. The conditions on the $\beta_i$ coefficients required for the stability of the various solutions for the order parameter are calculated. By considering the symmetries that are broken by the vortex solutions we are able to generate the moduli fields associated with the low energy excitations of the vortices. Using these fields we determine the effective free energy describing the dynamics of these excitations.