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Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids

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

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Claudio Furtado, A. M. de M. Carvalho, L. C. Garcia de Andrade, F. Moraes. 2004-01-08. Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids. https://arxiv.org/abs/gr-qc/0401025

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