Pseudo-relativistic fermionic systems with attractive Yukawa potential

TL;DR

This paper analyzes the stability and ground state properties of large pseudo-relativistic fermionic systems with attractive Yukawa interactions using Hartree-Fock theories, identifying critical mass thresholds for stability.

Contribution

It provides a rigorous stability criterion and explores ground state existence in different mass regimes for pseudo-relativistic fermions with Yukawa potential.

Findings

System stability depends on total mass relative to a critical value.

Existence and properties of ground states vary across sub-critical and critical mass regimes.

Theoretical framework established for pseudo-relativistic fermionic systems with attractive interactions.

Abstract

We study the Hartree-Fock and Hartree-Fock-Bogoliubov theories for a large fermionic system with the pseudo-relativistic kinetic energy and an attractive Yukawa interaction potential. We prove that the system is stable if and only if the total mass does not excess a critical value, and investigate the existence and properties of ground states in both sub-critical and critical mass regimes.