Vortex Dynamics, Resistivity Formula, and Fluctuation-dissipation Theorems

TL;DR

This paper examines the forces on moving vortices in superfluids and superconductors, clarifying conflicting results in literature by analyzing resistivity formulas, Berry's phase, and fluctuation-dissipation theorems.

Contribution

It identifies the invalidity of the relaxation time approximation in vortex force calculations and connects vortex dynamics to transport theory.

Findings

Relaxation time approximation is invalid for force calculations.

Clarification of the role of Berry's phase in vortex dynamics.

Discussion on fluctuation-dissipation theorems in this context.

Abstract

We investigate the problem of forces on moving vortex in a superfluid or superconductor. The main purpose is to locate the source which leads to the contradictory results in the literature. We establish the connection between this problem to the difficult but well studied subject of resistivity formula in transport theory. The relaxation time approximation used in the force calculation via force-force correlation function is shown to be invalid. The roles of Berry's phase and fluctuation-dissipation theorems are discussed.