Billiards correlation functions

Details Billiards correlation functions Billiards correlation functions

1993-10-27

arxiv.org/abs/chao-dyn/9310005v1

Journal of Statistical Physics 76, 549--586, 1994

Nonlinear Sciences

Chaotic Dynamics

25 pages, 27 figures, POSTSCRIPT, not encoded, 730K. Keywords: Billiards, correlation functions, velocity autocorrelation, dif

Scientific paper

We discuss various experiments on the time decay of velocity autocorrelation functions in billiards. We perform new experiments and find results which are compatible with an exponential mixing hypothesis, first put forward by [FM]: they do not seem compatible with the stretched exponentials believed, in spite of [FM], to describe the mixing. The analysis led us to several byproducts: we obtain information about the normal diffusive nature of the motion and we consider the probability distribution of the number of collisions in time $t_m$ (as $t_m\to\io$) finding a strong dependence on some geometric characteristics of the locus of the billiards obstacles.

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