Modular structures on trace class operators and applications to Landau levels

Fabio Bagarello, Honnouvo, S Twareque Ali

Risultato della ricerca: Article

23 Citazioni (Scopus)

Abstract

The energy levels, generally known as the Landau levels, which characterize the motion ofan electron in a constant magnetic field, are those of the one-dimensional harmonic oscillator,with each level being infinitely degenerate. We show in this paper how the associatedvon Neumann algebra of observables displays a modular structure in the sense of theTomita-Takesaki theory, with the algebra and its commutant referring to the two orientationsof the magnetic field. A KMS state can be built which in fact is the Gibbs state for anensemble of harmonic oscillators. Mathematically, the modular structure is shown to ariseas the natural modular structure associated to the Hilbert space of all Hilbert-Schmidtoperators.
Lingua originaleEnglish
Numero di pagine17
RivistaJOURNAL OF PHYSICS. A, MATHEMATICAL AND THEORETICAL
Volume43
Stato di pubblicazionePublished - 2010

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All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

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