ON THE GENERALIZED BOLTZMANN EQUATION OF A QUANTUM GAS

Journal Article · Sun Oct 01 00:00:00 EDT 1961 · Physica

DOI:https://doi.org/10.1016/0031-8914(61)90122-7· OSTI ID:4829439

Fujita, E

The generalized master equation for a quantum gas due to Resibois is analyzed with the aid of new diagrams, which are intimately related to operator diagrams invented by Prigogine and Resibois. lt is showvn that part of this equation, which is important for the derivation of generalized Boltzmann equation, has a form analogous to the Pauli equation with the probability of quantum statistical transition between many-body states, the probability being expressible in terms of a matrix A formally identical to the so-called transition matrix defined in the modern theory of potential scattering. By use of the technique devised for developing the binary collision expansion of the quantum statistical pair propagator, many-body elements of A are expanded in terms of two- body elements of A. The generalized Boltzmann equation or the reduced equation for the average occupation number of a single-particle momentum state is derived in an usual manner from the generalized master equation. It is pointed out that the UehlingUhlenbeck equation for a hard-sphere Fermi gas is valid only in the lowest order a/sup 2/, a being diameter of a hard sphere, at the very low temperatures. The new equation valid up to the order a/sup 2/(ap/sub f/h-sup 1/ ), p/sub f/ the Fermi momentum of an ideal Fermi gas and h Planck's constant, is given explicitely. Any higher order corrections could easily be calculated in the frame work of the theory. (auth)

• Research Organization: Universite, Brussels
• NSA Number: NSA-16-002357
• OSTI ID: 4829439
• Journal Information: Physica, Vol. Vol: 27; Other Information: Orig. Receipt Date: 31-DEC-62
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

PHYSICS
BOLTZMANN EQUATION
DIAGRAMS
DIFFERENTIAL EQUATIONS
ENTROPY
EQUATIONS
ERRORS
FERMI GAS
FERMIONS
GASES
INTERACTIONS
IRREVERSIBLE PROCESSES
MANY BODY PROBLEM
MATHEMATICS
MATRICES
MOMENTUM
OPERATORS
PAULI PRINCIPLE
PRIGOGINE THEOREM
PROBABILITY
QUANTUM MECHANICS
SCATTERING
SPHERES
STATISTICS
T-MATRIX
TEMPERATURE
THERMODYNAMICS
TRANSIENTS