Berry Phase in Semiclassical Dynamics of Bogoliubov Quasiparticles

We develop a semiclassical theory for Bogoliubov waves by following the motion of wave-packets in real and momentum spaces. Because of the interaction between atoms, the semiclassical dynamics of Bogoliubov quasiparticles are found to be modified by the Berry phase and are very different from single particle excitations in a noninteracting system. We use this semiclassical approach to study the scattering of phonons by a vortex in a superfluid and calculate the transverse as well as longitudinal forces on the vortex.