Anomalous diffusion in infinite horizon billiards

作     者：Douglas N. Armstead Brian R. Hunt Edward Ott 

作者机构：Department of Physics and Institute for Research in Electronics and Applied Physics University of Maryland College Park Maryland 20904 Department of Mathematics and Institute for Physical Science and Technology University of Maryland College Park Maryland 20904 Department of Physics Department of Electrical and Computer Engineering and Institute for Research in Electronics and Applied Physics University of Maryland College Park Maryland 20904 

出 版 物：《Physical Review E》 (物理学评论E辑：统计、非线性和软体物理学)

年 卷 期：2003年第67卷第2期

页      面：021110-021110页

核心收录：

学科分类：07[理学] 070203[理学-原子与分子物理] 0702[理学-物理学] 

基　　金：National Science Foundation, NSF Directorate for Mathematical and Physical Sciences, MPS, (0104087) Directorate for Mathematical and Physical Sciences, MPS 

主　　题：Diffusion 

摘      要：We consider the long time dependence for the moments of displacement 〈|r|q〉 of infinite horizon billiards, given a bounded initial distribution of particles. For a variety of billiard models we find 〈|r|q〉∼tγq (up to factors of lnt). The time exponent, γq, is piecewise linear and equal to q/2 for q2. We discuss the lack of dependence of this result on the initial distribution of particles and resolve apparent discrepancies between this time dependence and a prior result. The lack of dependence on initial distribution follows from a remarkable scaling result that we obtain for the time evolution of the distribution function of the angle of a particle’s velocity vector.