The Boltzmann-Grad limit of the periodic Lorentz gas

被引：44

作者：

Marklof, Jens ^{[1
]}

Strombergsson, Andreas ^{[2
]}

机构：

[1] Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England

[2] Uppsala Univ, Dept Math, SE-75106 Uppsala, Sweden

来源：

ANNALS OF MATHEMATICS | 2011年 / 174卷 / 01期

基金：

英国工程与自然科学研究理事会;

关键词：

FREE-PATH LENGTHS; SURE INVARIANCE-PRINCIPLE; SMALL-SCATTERER LIMIT; STATISTICAL PROPERTIES; INFINITE-HORIZON; RECURRENCE; SYSTEMS;

D O I：

10.4007/annals.2011.174.1.7

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the dynamics of a point particle in a periodic array of spherical scatterers and construct a stochastic process that governs the time evolution for random initial data in the limit of low scatterer density (Boltzmann-Grad limit). A generic path of the limiting process is a piecewise linear curve whose consecutive segments are generated by a Markov process with memory two.

引用

页码：225 / 298

页数：74

共 26 条

[1] Exponential Decay of Correlations in Multi-Dimensional Dispersing Billiards
Balint, Peter
Toth, Imre Peter
[J]. ANNALES HENRI POINCARE, 2008, 9 (07): : 1309 - 1369
[2] STATISTICAL PROPERTIES OF 2-DIMENSIONAL PERIODIC LORENTZ GAS WITH INFINITE HORIZON
BLEHER, PM
[J]. JOURNAL OF STATISTICAL PHYSICS, 1992, 66 (1-2) : 315 - 373
[3] The distribution of the free path lengths in the periodic two-dimensional Lorentz gas in the small-scatterer limit
Boca, Florin P.
Zaharescu, Alexandru
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2007, 269 (02) : 425 - 471
[4] ON THE BOLTZMANN-EQUATION FOR THE LORENTZ GAS
BOLDRIGHINI, C
BUNIMOVICH, LA
SINAI, YG
[J]. JOURNAL OF STATISTICAL PHYSICS, 1983, 32 (03) : 477 - 501
[5] On the distribution of free path lengths for the periodic Lorentz gas
Bourgain, J
Golse, F
Wennberg, B
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1998, 190 (03) : 491 - 508
[6] Bunimovich L., 1980, COMMUN MATH PHYS, V78, P479, DOI DOI 10.1007/BF02046760
[7] On the distribution of free path lengths for the periodic Lorentz gas III
Caglioti, E
Golse, F
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2003, 236 (02) : 199 - 221
[8] The Boltzmann-Grad limit of the periodic Lorentz gas in two space dimensions
Caglioti, Emanuele
Golse, Francois
[J]. COMPTES RENDUS MATHEMATIQUE, 2008, 346 (7-8) : 477 - 482
[9] STATISTICAL PROPERTIES OF THE PERIODIC LORENTZ GAS - MULTIDIMENSIONAL CASE
CHERNOV, NI
[J]. JOURNAL OF STATISTICAL PHYSICS, 1994, 74 (1-2) : 11 - 53
[10] The Lyapunov exponent in the Sinai billiard in the small scatterer limit
Dahlqvist, P
[J]. NONLINEARITY, 1997, 10 (01) : 159 - 173

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