The Global Minimum of the Effective Potential of the Many-Electron System with Delta-Interaction

TL;DR

This paper proves that the lowest energy state of a many-electron system with delta-interaction aligns with the BCS mean field solution, using bounds derived from Hadamard's inequality.

Contribution

It establishes the global minimum of the effective potential as the BCS mean field configuration through a novel bound and Taylor expansion analysis.

Findings

The global minimum corresponds to the BCS mean field.

A simple bound is derived using Hadamard's inequality.

Second order Taylor expansion around the minimum is computed.

Abstract

We prove that the global minimum of the real part of the full effective potential of the many-electron system with attractive delta-interaction is in fact given by the BCS mean field configuration. This is a consequence of a simple bound which is obtained by applying Hadamard's inequality to the functional determinant. The second order Taylor expansion around the minimum is computed.