From Feynman's Wave Function to the Effective Theory of Vortex Dynamics

TL;DR

This paper derives an effective theory for vortex dynamics in superfluids by analyzing wave function overlaps, confirming the finite vortex mass and reconciling phenomenological models with microscopic calculations.

Contribution

It provides a microscopic derivation of vortex dynamics, clarifying the effective mass and validating phenomenological approaches through wave function overlap calculations.

Findings

Vortex effective mass is finite.

Microscopic results align with phenomenological models.

Vortices experience Magnus force and weak sound wave interactions.

Abstract

We calculate the overlap between two many-body wave functions for a superfluid film containing a vortex at shifted positions. Comparing the results to phenomenological theories, which treat vortices as point particles, we find that the results are consistent if the point-particle vortices are considered as under the action of the Magnus force and in weak interaction with sound waves of the superfluid. We are then able to resolve the disagreement concerning the effective mass of vortices, showing it is finite.