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

Mayorga-Zambrano, Juan; Felmer, Patricio; Dolbeault, Jean

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

Publisher

Springer

Pages

43-66

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