Evolution from BCS Superconductivity to Bose Condensation: Analytic Results for the crossover in three dimensions

TL;DR

This paper presents an analytic solution for the BCS to Bose-Einstein condensation crossover in three dimensions, providing clear insights into the evolution of physical quantities at zero temperature.

Contribution

It offers the first complete analytic solution for the mean-field and Gaussian-level equations describing the BCS-BEC crossover in 3D free fermions with contact interactions.

Findings

Analytic expressions for physical quantities across the crossover.

Verification of the smooth evolution without singularities.

Explicit use of elliptic integrals for solution.

Abstract

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution.