Orbitally stable states in generalized Hartree-Fock theory
Résumé
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.
Mots clés
compact self-adjoint operators
trace-class operators
mixed states
occupation numbers
Lieb-Thirring inequality
Schrödinger operator
asymptotic distribution of eigenvalues
free energy
temperature
entropy
Hartree-Fock model
self-consistent potential
orbital stability
nonlinear equation
loss of compactness
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