On the decay of correlations in Sinai billiards with infinite horizon

Details On the decay of correlations in Sinai billiards with infinite horizon On the decay of correlations in Sinai billiards with infinite horizon

1996-01-18

arxiv.org/abs/chao-dyn/9601013v1

Nonlinear Sciences

Chaotic Dynamics

6 pages LaTeX, 5 postscript figures

Scientific paper

10.1016/0375-9601(96)00404-5

We compute the decay of the autocorrelation function of the observable $|v_x|$ in the Sinai billiard and of the observable $v_x$ in the associated Lorentz gas with an approximation due to Baladi, Eckmann and Ruelle. We consider the standard configuration where the disks is centered inside a unit square. The asymptotic decay is found to be $C(t) \sim c(R)/t$. An explicit expression is given for the prefactor $c(R)$ as a function of the radius of the scatterer. For the small scatterer case we also present expressions for the preasymptotic regime. Our findings are supported by numerical computations.

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