Stability of the Hartree-Fock model with temperature

TL;DR

This paper investigates the stability and existence of minimizers in the Hartree-Fock model at finite temperature, showing how solutions behave as temperature varies and establishing orbital stability.

Contribution

It introduces a variational framework for the Hartree-Fock model with temperature and analyzes the conditions for minimizer existence and stability.

Findings

Minimizers exist for total charge below a temperature-dependent threshold

The zero temperature limit recovers the classical Hartree-Fock model

Orbital stability of solutions is established through a variational approach

Abstract

This paper is devoted to the Hartree-Fock model with temperature in the euclidean space. For large classes of free energy functionals, minimizers are obtained as long as the total charge of the system does not exceed a threshold which depends on the temperature. The usual Hartree-Fock model is recovered in the zero temperature limit. An orbital stability result for the Cauchy problem is deduced from the variational approach.