Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

Details Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions

1995-01-02

arxiv.org/abs/chao-dyn/9501001v1

Nonlinear Sciences

Chaotic Dynamics

14 pages LaTeX, figs 2-3 on .uu file, fig 1 available from author

Scientific paper

10.1007/BF02179657

We compute the Lyapunov exponent, generalized Lyapunov exponents and the diffusion constant for a Lorentz gas on a square lattice, thus having infinite horizon. Approximate zeta functions, written in terms of probabilities rather than periodic orbits, a re used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relation between the analytic structure of the zeta function, where a branch cut plays an important role, and the asymptotic dynamics of the system. We find a diverging diffusion constant $D(t) \sim \log t$ and a phase transition for the generalized Lyapunov exponents.

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