Quantum-statistical kinetic equations

Journal Article · Sat Jul 01 00:00:00 EDT 1989 · Journal of Statistical Physics; (USA)

DOI:https://doi.org/10.1007/BF01044240· OSTI ID:7243727

Loss, D; Schoeller, H ^[1]

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1. Universitaet Zuerich (Switzerland)

Considering a homogeneous normal quantum fluid consisting of identical interacting fermions or bosons, the authors 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{sub q}-rule, etc.) to nonequilibrium systems described by a density operator {rho}(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.

• OSTI ID: 7243727
• Journal Information: Journal of Statistical Physics; (USA), Vol. 56:1-2; ISSN 0022-4715
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
KINETIC EQUATIONS
STATISTICAL MECHANICS
QUANTUM FLUIDS
BOLTZMANN EQUATION
BOLTZMANN-VLASOV EQUATION
BOSE-EINSTEIN STATISTICS
BOSONS
COLLISIONS
FACTORIZATION
FERMI STATISTICS
FERMIONS
HELIUM 3
HELIUM 4
LAPLACE TRANSFORMATION
MARKOV PROCESS
PROJECTION OPERATORS
QUANTUM MECHANICS
RENORMALIZATION
SERIES EXPANSION
SUPEROPERATORS
DIFFERENTIAL EQUATIONS
EQUATIONS
EVEN-EVEN NUCLEI
EVEN-ODD NUCLEI
FLUIDS
HELIUM ISOTOPES
INTEGRAL TRANSFORMATIONS
ISOTOPES
LIGHT NUCLEI
MATHEMATICAL OPERATORS
MECHANICS
NUCLEI
PARTIAL DIFFERENTIAL EQUATIONS
STABLE ISOTOPES
STOCHASTIC PROCESSES
TRANSFORMATIONS
640450* - Fluid Physics- Superfluidity
640460 - Fluid Physics- Other Quantum Fluids
657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics