BASIS OF THE FUNCTIONAL ASSUMPTION IN THE THEORY OF THE BOLTZMANN EQUATION

Journal Article · Fri Nov 01 04:00:00 EST 1963 · Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D

DOI:https://doi.org/10.1103/PhysRev.132.1388· OSTI ID:4686337

Green, M S; Piccirelli, R A

The long-time behavior of the n-particle probability densities for a large, dilute system of point particles interacting with short-range repulsive forces is studied. The main result is an exact series for the n-particle density that consists of two parts. The first part is a timeindependent functional of the singlet density that is expressed as a functional power series and that is a direct analog of the equilibrium density series. The second part is also a functional power series in the singlet density but the coefficients depend on time and on the initial correlations. The coefficients of both series are given explicitly in terms of operators that are determined by the dynamics of isolated groups of particles. It is demonstrated that these operators vanish for phase points corresponding to motions during which there are two or more groups of particles that either are statistically and dynamically independent or are such that each of them is dynamically connected to the rest by no more than one particle. It is argued that all the terms of the exact series are finite and that the terms of second part (the error) decrease with increasing time so that the first part is the asymptotic form proposed by Bogoliubov. The relevance of the results for the Boltzmann equation is indicated. A form of the Boltzmann collision integral that is valid in the steady state and to all orders of the density is described. (auth)

• Research Organization: National Bureau of Standards, Washington, D.C.
• NSA Number: NSA-17-041631
• OSTI ID: 4686337
• Journal Information: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D, Journal Name: Physical Review (U.S.) Superseded in part by Phys. Rev. A, Phys. Rev. B: Solid State, Phys. Rev. C, and Phys. Rev. D Vol. Vol: 132; ISSN PHRVA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

BOLTZMANN EQUATION
DIFFERENTIAL EQUATIONS
ERRORS
INTERACTIONS
MANY BODY PROBLEM
MATHEMATICS
MOTION
OPERATORS
PARTICLE MODELS
PHYSICS
QUANTUM MECHANICS