Macroscopic Dynamics of the Strong-Coupling BCS-Hubbard Model

TL;DR

This paper demonstrates the dynamical behavior of the strong-coupling BCS-Hubbard model, illustrating how long-range interactions and Coulomb repulsion influence superconductivity in fermionic systems.

Contribution

It provides a simple, rigorous example of the dynamical properties of fermions with mean-field interactions, emphasizing the role of Coulomb repulsion in superconductivity.

Findings

Coulomb repulsion impacts superconducting properties.

Long-range interactions are rigorously analyzed.

The model is pedagogical and physically relevant.

Abstract

The aim of the current paper is to illustrate, in a simple example, our recent, very general, rigorous results [Bru J.-B., de Siqueira Pedra W., J. Math. Anal. Appl. (2020), doi.org: 10.1016/j.jmaa.2020.124434 and 10.1016/j.jmaa.2020.124517] on the dynamical properties of fermions and quantum-spin systems with long-range, or mean-field, interactions, in infinite volume. We consider here the strong-coupling BCS-Hubbard model, because this example is very pedagogical and, at the same time, physically relevant for it highlights the impact of the (screened) Coulomb repulsion on ($s$-wave) superconductivity.