ISSN:
1572-9613
Keywords:
Kinetic equations
;
exchange effects
;
renormalized cluster series
;
quantum-statistical Boltzmann and Choh-Uhlenbeck equations
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01044240
Permalink
