Abstract
Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, we derive an exact quantum-statistical generalized kinetic equation with a collision operator given as explicit cluster series where exchange effects are included through renormalized Liouville operators. This new result is obtained by applying a recently developed superoperator formalism (Liouville operators, cluster expansions, symmetrized projectors,P q rule, etc.) to nonequilibrium systems described by a density operatorρ(t) which obeys the von Neumann equation. By means of this formalism a factorization theorem is proven (being essential for obtaining closed equations), and partial resummations (leading to renormalized quantities) are performed. As an illustrative application, the quantum-statistical versions (including exchange effects due to Fermi-Dirac or Bose-Einstein statistics) of the homogeneous Boltzmann (binary collisions) and Choh-Uhlenbeck (triple collisions) equations are derived.
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Loss, D., Schoeller, H. Quantum-statistical kinetic equations. J Stat Phys 56, 175–201 (1989). https://doi.org/10.1007/BF01044240
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DOI: https://doi.org/10.1007/BF01044240