Orbitally-Stable States in Generalized Hartree-Fock Theory

Dolbeault, Jean; Felmer, Patricio; Lewin, Mathieu

Dolbeault, Jean; Felmer, Patricio; Lewin, Mathieu (2009), Orbitally-Stable States in Generalized Hartree-Fock Theory, Mathematical Models and Methods in Applied Sciences, 19, 3, p. 347-367. http://dx.doi.org/10.1142/S0218202509003450

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00250383/en/

Date

2009

Journal name

Mathematical Models and Methods in Applied Sciences

Volume

Number

Publisher

World Scientific

Pages

347-367

Abstract (EN)

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.

Subjects / Keywords

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