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

被引：0
作者：
J. Dolbeault
P. Felmer
J. Mayorga-Zambrano
机构：
[1] Ceremade Université Paris Dauphine,
[2] Universidad de Chile,undefined
来源：
Monatshefte für Mathematik | 2008年 / 155卷
关键词：
2000 Mathematics Subject Classification: 81Q10, 82B10; 26D15, 35J10, 47B34; Key words: 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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摘要：
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.
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