  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.
