Cumulant solution of the elastic Boltzmann transport equation in an infinite uniform medium

Journal Article · Sat Apr 01 04:00:00 EST 2000 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

DOI:https://doi.org/10.1103/PhysRevE.61.3871· OSTI ID:20216091

Cai, W ^[1]; Lax, M ^[1]; Alfano, R R ^[1]

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1. Institute for Ultrafast Spectroscopy and Lasers, New York State Center of Advanced Technology for Ultrafast Photonic Materials and Applications, Department of Physics, The City College and Graduate Center of City University of New York, New York, New York 10031 (United States)

We consider an analytical solution of the time-dependent elastic Boltzmann transport equation in an infinite uniform isotropic medium with an arbitrary phase function. We obtain (1) the exact distribution in angle, (2) the exact first and second spatial cumulants at any angle, and (3) an approximate combined distribution in position and angle and a spatial distribution whose central position and half-width of spread are always exact. The resulting Gaussian distribution has a center that advances in time, and an ellipsoidal contour that grows and changes shape providing a clear picture of the time evolution of the particle migration from near ballistic, through snakelike and into the final diffusive regime. (c) 2000 The American Physical Society.

• OSTI ID: 20216091
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics Journal Issue: 4 Vol. 61; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ANALYTICAL SOLUTION
BOLTZMANN EQUATION
CORRELATION FUNCTIONS
DISTRIBUTION FUNCTIONS
GAUSS FUNCTION
THEORETICAL DATA
TRANSPORT THEORY