Derivation of hydrodynamics for the gapless mode in the BEC-BCS crossover from the exact one-loop effective action

TL;DR

This paper derives hydrodynamic properties of the BEC-BCS crossover at zero temperature from the exact one-loop effective action, providing a unified approach to sound velocity and superfluid equations.

Contribution

It introduces a method to extract hydrodynamics directly from the exact one-loop effective action in the BEC-BCS crossover.

Findings

Calculated the sound velocity across BCS and BEC regimes.

Derived generalized superfluid continuity equations.

Showed the effectiveness of the derivative expansion approach.

Abstract

We show that many hydrodynamical properties of the BEC/BCS crossover in the presence of a Feshbach resonance at T=0 can be derived easily from the derivative expansion of the (exact) fully renormalized one-loop effective action. In particular, we calculate the velocity of sound throughout the BCS and BEC regimes and derive the generalized superfluid continuity equations for the composite two-fluid system.