On non-Riemannian geometry of superfluids

TL;DR

This paper extends the Gross-Pitaevski equation for superfluids to non-Riemannian spacetime with torsion, revealing effects like flow damping and phase shifts, thus exploring geometric influences on superfluid dynamics.

Contribution

It introduces a non-Riemannian geometric framework to superfluid theory, analyzing torsion effects on flow and phase phenomena in superfluids.

Findings

Torsion induces damping in superfluid flow velocity.

A cylindrically symmetric solution with constant torsion is derived.

Torsion affects the Sagnac phase shift in superfluid systems.

Abstract

The Gross-Pitaevski (GP) equation describing helium superfluids is extended to non-Riemannian spacetime background where torsion is shown to induce the splitting in the potential energy of the flow. A cylindrically symmetric solution for Minkowski background with constant torsion is obtained which shows that torsion induces a damping on the superfluid flow velocity. The Sagnac phase shift is computed from the superfluid flow velocity obtained from the solution of GP equations.