Lyapunov exponents and anomalous diffusion of a Lorentz gas with infinite horizon using approximate zeta functions
- Royal Inst. of Technology, Stockholm (Sweden)
We compute the Lyapunov exponent, the 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, are used in order to avoid the convergence problems of cycle expansions. The emphasis is on the relaxation between the analytic structure of the zeta function, where a branch cut plays an important role, and the asymptotic dynamics of the system. The Lyapunov exponent for the corresponding map agrees with the conjectured limit {lambda}{sub map}=-2 log(R) + C + O(R) and we derive an approximate value for the constant C in good agreement with numerical simulations. We also find a diverging diffusion constant D(t){approx}log t and a phase transition for the generalized Lyapunov exponents.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 471872
- Journal Information:
- Journal of Statistical Physics, Journal Name: Journal of Statistical Physics Journal Issue: 3-4 Vol. 84; ISSN JSTPBS; ISSN 0022-4715
- Country of Publication:
- United States
- Language:
- English
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