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Journal of Statistical Physics

, Volume 89, Issue 3–4, pp 633–653 | Cite as

Algebraic structure of quantum fluctuations

  • B. Momont
  • A. Verbeure
  • V. A. Zagrebnov
Article

Abstract

On the basis of the existence of second and third moments of fluctuations, we prove a theorem about the Lie-algebraic structure of fluctuation operators. This result gives insight into the quantum character of fluctuations. We illustrate the presence of a Lie algebra of fluctuation operators in a model of the anharmonic crystal, and show the dependence of the Lie-algebra structure on the fine structure of the fluctuation operator algebra. The result is also applied to construct the normal Goldstone mode in the ideal Bose gas for Bose-Einstein condensation

Key Words

Quantum fluctuations Lie-algebraic structure extremal states Goldstone theorem 

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Copyright information

© Plenum Publishing Corporation 1997

Authors and Affiliations

  1. 1.Instituut voor Theoretische FysicaK.U. LeuvenLeuvenBelgium
  2. 2.Département de PhysiqueUniversité de la Méditerranée (Aix-Marseille II) and Centre de Physique Théorique, CNRS-LuminyMarseille Cedex 09France

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