On the decay of correlations in Sinai billiards with infinite horizon

Abstract

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.

6 pages LaTeX, 5 postscript figures

References in corpus (3)

• The Lyapunov exponent in the Sinai billiard in the small scatterer limit
• Approximate zeta functions for the Sinai billiard and related systems
• Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

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