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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00088819/en/Date
2008Journal name
Monatshefte für MathematikVolume
155Number
1Publisher
Springer
Pages
43-66
Publication identifier
Metadata
Show full item recordAbstract (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 resultsRelated items
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