Extended Fluid–Dynamics and Collective Motion of Two Trapped Fermion Species with Pairing Interactions

Abstract

We extend our earlier fluid–dynamical description of fermion superfluids incorporating the particle energy flow together with the equation of motion for the internal kinetic energy of the pairs. The formal scheme combines a set of equations similar to those of classical hydrodynamics with the equations of motion for the anomalous density and for its related momentum density and kinetic energy density. This dynamical frame represents a second order truncation of an infinite hierarchy of equations of motion isomorphic to the full time dependent Hartree–Fock–Bogoliubov equations in coordinate representation. We analyze the equilibrium solutions and fluctuations for a homogeneous, unpolarized fermion system of two species, and show that the collective spectrum presents the well-known Anderson–Bogoliubov low energy mode of homogeneous superfluids and a pairing vibration near the gap energy.