Date
2006
Notes
New references added
Dewey
Probabilités et mathématiques appliquées
Sujet
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
Journal issue
Journal of Functional Analysis
Volume
238
Number
1
Publication date
2006
Article pages
193-220
Publisher
Elsevier
Author
Paturel, Eric
Dolbeault, Jean
Felmer, Patricio
Loss, Michael
Type
Article accepté pour publication ou publié
Abstract (EN)
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.
