Compactness properties for trace-class operators and applications to quantum mechanics
Résumé
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.
Mots clés
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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