Compactness properties for trace-class operators and applications to quantum mechanics

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Date
2008
Link to item file
http://hal.archives-ouvertes.fr/hal-00088819/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
Compact self-adjoint operators; Trace-class operators; mixed states; occupation numbers; Lieb-Thirring inequality; Gagliardo-Nirenberg inequality; logarithmic Sobolev inequality; optimal constants; orthonormal and sub-orthonormal systems; Schrödinger operator; asymptotic distribution of eigenvalues; free energy; embeddings; compactness results
Journal issue
Monatshefte für Mathematik
Volume
155
Number
1
Publication date
2008
Article pages
43-66
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00605-008-0533-5
URI
https://basepub.dauphine.fr/handle/123456789/544
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Author
Mayorga-Zambrano, Juan
Felmer, Patricio
Dolbeault, Jean
Type
Article accepté pour publication ou publié
Abstract (EN)
Interpolation inequalities of Gagliardo-Nirenberg type and compactness results for self-adjoint trace-class operators with finite kinetic energy are established. Applying these results to the minimization of various free energy functionals, we determine for instance stationary states of the Hartree problem with temperature corresponding to various statistics.