Superfluid hydrodynamics of polytropic gases:dimensional reduction and sound velocity

摘要

Motivated by the fact that two-component confined fermionic gases inBardeen-Cooper-Schrieffer-Bose-Einstein condensate (BCS-BEC) crossover can bedescribed through an hydrodynamical approach, we study these systems - both inthe cigar-shaped configuration and in the disk-shaped one - by using apolytropic Lagrangian density. We start from the Popov Lagrangian density andobtain, after a dimensional reduction process, the equations that control thedynamics of such systems. By solving these equations we study the soundvelocity as a function of the density by analyzing how the dimensionalityaffects this velocity