Journal of Statistical Physics

, Volume 54, Issue 3–4, pp 765–795 | Cite as

A new quantum statistical evaluation method for time correlation functions

  • D. Loss
  • H. Schoeller


Considering a system ofN identical interacting particles, which obey Fermi-Dirac or Bose-Einstein statistics, we derive new formulas for correlation functions of the type\(C(t) = \langle \Sigma _{i = 1}^N A_i (t) \Sigma _{j = 1}^N B_j \rangle \) (whereBj is diagonal in the free-particle states) in the thermodynamic limit. Thereby we apply and extend a superoperator formalism, recently developed for the derivation of long-time tails in semiclassical systems. As an illustrative application, the Boltzmann equation value of the time-integrated correlation functionC(t) is derived in a straightforward manner. Due to exchange effects, the obtained t-matrix and the resulting scattering cross section, which occurs in the Boltzmann collision operator, are now functionals of the Fermi-Dirac or Bose-Einstein distribution.

Key words

Time correlation functions Liouville operators cluster expansion exchange effects 


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Copyright information

© Plenum Publishing Corporation 1989

Authors and Affiliations

  • D. Loss
    • 1
  • H. Schoeller
    • 1
  1. 1.Institut für Theoretische Physik der Universität ZürichZürichSwitzerland

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