Monatshefte für Mathematik

, 155:43 | Cite as

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

  • J. Dolbeault
  • P. Felmer
  • J. Mayorga-Zambrano


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.

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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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • J. Dolbeault
    • 1
  • P. Felmer
    • 2
  • J. Mayorga-Zambrano
    • 2
  1. 1.Ceremade Université Paris DauphineParisFrance
  2. 2.Universidad de ChileSantiagoChile

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