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

Mayorga-Zambrano, Juan; Felmer, Patricio; Dolbeault, Jean (2008), Compactness properties for trace-class operators and applications to quantum mechanics, Monatshefte für Mathematik, 155, 1, p. 43-66. http://dx.doi.org/10.1007/s00605-008-0533-5

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00088819/en/
Date
2008
Journal name
Monatshefte für Mathematik
Volume
155
Number
1
Publisher
Springer
Pages
43-66
Publication identifier
http://dx.doi.org/10.1007/s00605-008-0533-5
Metadata
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Author(s)
Mayorga-Zambrano, Juan
Felmer, Patricio
Dolbeault, Jean cc
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.
Subjects / Keywords
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

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