Date
2006
Description
New references added
Indexation documentaire
Probabilités et mathématiques appliquées
Subject
Gagliardo-Nirenberg inequalities for systems; systems of nonlinear Schrödinger equations; free energy; dynamical stability in quantum systems; occupation numbers; mixed states; stability of matter; Weyl asymptotics; asymptotic distribution of eigenvalues; Schrödinger operator; Lieb-Thirring inequality; optimal constants; Gagliardo-Nirenberg inequality; orthonormal and sub-orthonormal systems; Gamma function; logarithmic Sobolev inequality
Nom de la revue
Journal of Functional Analysis
Volume
238
Numéro
1
Date de publication
2006
Pages article
193-220
Nom de l'éditeur
Elsevier
Auteur
Paturel, Eric
Dolbeault, Jean
Felmer, Patricio
Loss, Michael
Type
Article accepté pour publication ou publié
Résumé en anglais
We prove a Lieb-Thirring type inequality for potentials such that the associated Schrödinger operator has a pure discrete spectrum made of an unbounded sequence of eigenvalues. This inequality is equivalent to a generalized Gagliardo-Nirenberg inequality for systems. As a special case, we prove a logarithmic Sobolev inequality for infinite systems of mixed states. Optimal constants are determined and free energy estimates in connection with mixed states representations are also investigated.
