Journal of Statistical Physics

, Volume 14, Issue 4, pp 359–380 | Cite as

Quantum statistical hierarchy equation in nonequilibrium systems

  • Nobuhiko Mishima
  • Tomio Yamakoshi Petrosky
  • Miwae Yamazaki


An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived.

Key words

Wigner distribution function Fourier expansion method quantum statistical hierarchy equation diagrammatic method movable and unmovable contractions 


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Copyright information

© Plenum Publishing Corporation 1976

Authors and Affiliations

  • Nobuhiko Mishima
    • 1
  • Tomio Yamakoshi Petrosky
    • 2
  • Miwae Yamazaki
    • 3
  1. 1.Department of PhysicsTokyo Gakugei UniversityTokyoJapan
  2. 2.Department of PhysicsScience University of TokyoTokyoJapan
  3. 3.Department of PhysicsSaitama UniversitySaitamaJapan

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