Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids

TL;DR

This paper explores the geometric and topological phases, including the Aharonov-Bohm effect and Berry phase, for phonons in superfluids, drawing analogies with cosmic strings and using holonomy transformations.

Contribution

It introduces a geometric framework to analyze phonon phases in superfluids, highlighting the roles of holonomy and gravitational analogs of the Aharonov-Bohm effect.

Findings

Holonomy transformations characterize the phonon 'space-time' around vortices.

Both rotational and translational holonomies contribute to the Aharonov-Bohm effect.

Berry phase for phonons is also analyzed in this geometric context.

Abstract

In this article we discuss the analogy between superfluids and a spinning thick cosmic string. We use the geometrical approach to obtain the geometrical phases for a phonon in the presence of a vortex. We use loop variables for a geometric description of Aharonov-Bohm effect in these systems. We use holonomy transformations to characterize globally the "space-time" of a vortex and in this point of view we study the gravitational analog of the Aharonov-Bohm effect in this system. We demonstrate that in the general case the Aharonov-Bohm effect has a contribution both from the rotational and the translational holonomy. We study also Berrys quantum phase for phonons in this systems.