Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids
General Relativity and Quantum Cosmology
2007-05-23 v1
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.
Cite
@article{arxiv.gr-qc/0401025,
title = {Holonomy, Aharonov-Bohm effect and phonon scattering in superfluids},
author = {Claudio Furtado and A. M. de M. Carvalho and L. C. Garcia de Andrade and F. Moraes},
journal= {arXiv preprint arXiv:gr-qc/0401025},
year = {2007}
}
Comments
15 pages, Revtex4