Geometric Phase for Fermionic Quasiparticles Scattering by Disgyration in Superfluids

We consider a Volovik's analog model for description of a topological defects in a superfluid and we investigate the scattering of quasiparticles in this background. The analog of the gravitational Aharonov-Bohm in this system is found. An analysis of this problem employing loop variables is considered and corroborates for the existence of the Aharonov-Bohm effect in this system. The results presented here may be used to study the Aharonov-Bohm effect in superconductors.