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

Abstract:

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. © 2008 Springer-Verlag.

Año de publicación:

2008

Keywords:

• Mixed states
• Orthonormal and sub-orthonormal systems
• Gagliardo-Nirenberg inequality
• Lieb-Thirring inequality
• Logarithmic Sobolev inequality
• Occupation numbers
• Trace-class operators
• Compact self-adjoint operators
• Optimal constants

Fuente:

scopus