Dynamics of Bose-Einstein condensates of fermion pairs in the low density limit of BCS theory

TL;DR

This paper demonstrates that in the low-density limit, the evolution of fermion pair condensates in BCS theory can be effectively described by a time-dependent Gross-Pitaevskii equation, linking fermionic and bosonic descriptions.

Contribution

It establishes a rigorous approximation of BCS pair dynamics by a Gross-Pitaevskii equation in the dilute limit, bridging fermionic and bosonic models.

Findings

The pair density evolution is well-approximated by the Gross-Pitaevskii equation.

The approximation holds in the dilute, low-density limit of BCS theory.

Provides a mathematical connection between fermionic BCS and bosonic condensate descriptions.

Abstract

We show that the time-evolution of the wave function describing the macroscopic variations of the pair density in BCS theory can be approximated, in the dilute limit, by a time-dependent Gross-Pitaevskii equation.