Statistical properties of two-dimensional periodic Lorentz gas with infinite horizon

The author studies the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. He considers a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. He assumes that the initial position of the particle...

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Bibliographic Details
Published in:Journal of statistical physics 1992, Vol.66 (1-2), p.315-373
Main Author: BLEHER, P. M
Format: Article
Language:English
Subjects:
990200 > Mathematics & Computers
CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY
CRYSTAL LATTICES
CRYSTAL STRUCTURE
ELASTIC SCATTERING
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
FLUIDS
FULLY IONIZED GASES
GASES
GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE
IONIZED GASES
LIOUVILLE THEOREM
LORENTZ GAS
MATHEMATICAL MODELS
MOBILITY
PARTICLE MOBILITY
Physics
SCATTERING 665000 > Physics of Condensed Matter-- (1992-)
STATISTICAL MODELS
Statistical physics, thermodynamics, and nonlinear dynamical systems
TWO-DIMENSIONAL CALCULATIONS
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Summary:The author studies the asymptotic statistical behavior of the 2-dimensional periodic Lorentz gas with an infinite horizon. He considers a particle moving freely in the plane with elastic reflections from a periodic set of fixed convex scatterers. He assumes that the initial position of the particle in the phase space is random with uniform distribution with respect to the Liouville measure of the periodic problem. Interest is in the asymptotic statistical behavior of the particle displacement in the plane as the time t goes to infinity. It is assumed that the particle horizon is infinite, which means that the length of free motion of the particle is unbounded. It is shown that under some natural assumptions on the free motion vector autocorrelation function, the limit distribution of the particle displacement in the plane is Gaussian, but the normalization factor is (t log t){sup 1/2} and not t{sup 1/2} as in the classical case. The covariance matrix of the limit distribution is found.
ISSN:0022-4715
1572-9613
DOI:10.1007/BF01060071