# A lower bound for the BCS functional with boundary conditions at infinity

## TL;DR

This paper establishes a lower bound for the BCS functional with boundary conditions at infinity, linking it to Ginzburg-Landau type expressions, advancing understanding of fermionic systems in quantum physics.

## Contribution

It introduces a novel lower bound for the BCS functional considering boundary conditions at infinity, connecting microscopic BCS theory to macroscopic Ginzburg-Landau models.

## Key findings

- Derived a lower bound for the BCS energy functional.
- Connected BCS functional to Ginzburg-Landau expressions.
- Provided insights into fermionic systems with boundary conditions.

## Abstract

We consider a many-body system of fermionic atoms interacting via a local pair potential and subject to an external potential within the framework of BCS theory. We measure the free energy of the whole sample with respect to the free energy of a reference state which allows us to define a BCS functional with boundary conditions at infinity. Our main result is a lower bound for this energy functional in terms of expressions that typically appear in Ginzburg-Landau functionals.