Non-Riemannian acoustic spacetime and Magnus field in rotating Bose-Einstein condensates

TL;DR

This paper explores a teleparallel geometric framework for acoustic spacetime in rotating Bose-Einstein condensates, revealing how acoustic torsion influences phonon trajectories and mimics effects like the Meissner phenomenon.

Contribution

It introduces a teleparallel Riemannian geometry approach to acoustic spacetime in BECs, linking acoustic torsion with vortex dynamics and the Magnus field.

Findings

Acoustic torsion acts as a diverging lens on phonon trajectories.

The Magnus field cancels when acoustic torsion matches the condensate rotation.

The framework constrains physical parameters in rotating BECs.

Abstract

The teleparallel $T_{4}$ version of Riemannian geometry of acoustic spacetime in rotating $2-D$ Bose-Einstein condensates (BEC) is investigated. An experiment is proposed on the basis of phonon ray trajectory around a vortex. The deviation geodesic equation may be expressed in terms of Cartan acoustic torsion. The Riemann curvature is computed in terms of rotation of the fluid. The geodesic deviation equation shows that the acoustic torsion acts locally as a diverging lens and the stream lines on opposite sides of the BEC vortex flow apart from each other. We also show that the Magnus field is cancelled when the acoustic torsion coincides with the rotation of the condensate. This effect is equivalent to the Meissner effect in superconductors. It is interesting to note how the teleparallel acoustic spacetime constrains the physical parameters in the BEC. Here we use the term acoustic torsion since in teleparallelism it is derived from the acoustic metric.