Billiards correlation functions
Abstract
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 (as ) finding a strong dependence on some geometric characteristics of the locus of the billiards obstacles.
Cite
@article{arxiv.chao-dyn/9310005,
title = {Billiards correlation functions},
author = {Garrido Pedro and Gallavotti Giovanni},
journal= {arXiv preprint arXiv:chao-dyn/9310005},
year = {2008}
}
Comments
25 pages, 27 figures, POSTSCRIPT, not encoded, 730K. Keywords: Billiards, correlation functions, velocity autocorrelation, diffusion coefficients, Lorentz model, mixing, ergodic theory, chaos, Lyapunov exponents, numerical experiments