Transverse force on a moving vortex with the acoustic geometry

TL;DR

This paper explores the transverse force on a moving vortex within an acoustic spacetime framework, demonstrating that it aligns with the classical Magnus force using topological current theory and effective geometry.

Contribution

It introduces a novel approach by applying acoustic geometry and topological current theory to analyze vortex dynamics and the Magnus force in condensed matter systems.

Findings

The transverse force on a vortex matches the classical Magnus force.

Effective spacetime geometry naturally describes vortex behavior.

The approach bridges condensed matter physics with topological and geometric methods.

Abstract

We consider the transverse force on a moving vortex with the acoustic metric using the $\phi $-mapping topological current theory. In the frame of effective spacetime geometry the vortex appear naturally by virtue of the vortex tensor in the Lorentz spacetime and we show that it is just the vortex derived with the order parameter in the condensed matter. With the usual Lagrangian we obtain the equation of motion for the vortex. At last, we show that the transverse force on the moving vortex in our equation is just the usual Magnus force in a simple model.