The spectrum of the Liouville-von Neumann operator in the Hilbert-Schmidt space

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10 Citations (Scopus)

Abstract

The singular continuous spectrum of the Liouville operator of quantum statistical physics is, in general, properly included in the difference of the spectral values of the singular continuous spectrum of the associated Hamiltonian. The absolutely continuous spectrum of the Liouvillian may arise from a purely singular continuous Hamiltonian. We provide the correct formulas for the spectrum of the Liouville operator and show that the decaying states of the singular continuous subspace of the Hamiltonian do not necessarily contribute to the absolutely continuous subspace of the Liouvillian.
Original languageEnglish
Pages (from-to)4106-4118
Number of pages13
JournalJournal of Mathematical Physics
Volume40
Issue number8
Publication statusPublished - Aug 1999

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Statistical and Nonlinear Physics

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