Decay of correlations, Lyapunov exponents and anomalous diffusion in the Sinai billiard

1995/10/31 by Per Dahlqvist, Dahlqvist, Per
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences #Quantum chaos and dynamical systems #Spectroscopy and Quantum Chemical Studies #chao-dyn #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9510020

8 pages LaTeX, one figure

arxiv created 1995/11/02 · openalex publication_date 1995/11/02 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We compute the decay of the velocity autocorrelation function, the Lyapunov exponent and the diffusion constant for the Sinai billiard within the framework of dynamical zeta functions. The asymptotic decay of the velocity autocorrelation function is found to be C(t) ∼ c(R)/t. The Lyapunov exponent for the corresponding map agrees with the conjectured limit λ_map → -2log(R)+C as R → 0 where C=1-4log 2+27/(2π²)⋅ ζ(3). The diffusion constant of the associated Lorentz gas is found to be divergent D(t) ∼ log t.

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