Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids

Furtado, Claudio; Carvalho, A. M. de M.; de Andrade, L. C. Garcia; Moraes, F.

Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids

Authors

Furtado, Claudio

Carvalho, A. M. de M.

de Andrade, L. C. Garcia

Moraes, F.

Description

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.
15 pages, Revtex4