Dynamics of T=0 BCS condensates

TL;DR

This paper demonstrates that the zero-temperature dynamics of BCS superfluids can be described by a nonlinear Schrödinger equation similar to the Gross-Pitaevskii equation, using fermion-bosonization techniques.

Contribution

It introduces a novel fermion-bosonization approach to derive a nonlinear Schrödinger equation for BCS superfluids at zero temperature, distinct from the traditional order parameter description.

Findings

Derives a galilean invariant nonlinear Schrödinger equation for T=0 BCS condensates.

Shows the equation's form parallels the Gross-Pitaevskii equation for Bose superfluids.

Clarifies that the wavefunction in this equation is not the superfluid order parameter.

Abstract

Fermi-surface bosonization is used to show that the long-wavelength, $T=0$, dynamics of a BCS superfluid or superconductor is described by a galilean invariant non-linear time-dependent Schr{\"o}dinger equation. This equation is of same form as the Gross-Pitaevskii equation for a Bose superfluid, but the ``wavefunction'' is {\it not} the superfluid order parameter.