Relativistic two-fluid hydrodynamics with quantized vorticity from the nonlinear Klein-Gordon equation

TL;DR

This paper develops a relativistic two-fluid superfluid model based on the nonlinear Klein-Gordon equation, incorporating quantized vorticity, vortex dynamics, and interactions with the normal fluid, with implications for numerical analysis and string theory duals.

Contribution

It introduces a novel relativistic two-fluid superfluid model using the nonlinear Klein-Gordon equation, including vortex dynamics and a dual string theory description.

Findings

Quantized vorticity emerges from singular solutions.

The model facilitates numerical analysis of vortex filaments.

Dual transformation links vortex dynamics to string theory.

Abstract

We consider a relativistic two-fluid model of superfluidity, in which the superfluid is described by an order parameter that is a complex scalar field satisfying the nonlinear Klein-Gordon equation (NLKG). The coupling to the normal fluid is introduced via a covariant current-current interaction, which results in the addition of an effective potential, whose imaginary part describes particle transfer between superfluid and normal fluid. Quantized vorticity arises in a class of singular solutions and the related vortex dynamics is incorporated in the modified NLKG, facilitating numerical analysis which is usually very complicated in the phenomenology of vortex filaments. The dual transformation to a string theory description (Kalb-Ramond) of quantum vorticity, the Magnus force and the mutual friction between quantized vortices and normal fluid are also studied.