Random Walks in the Standard Map

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Abstract
A random walk description of enhanced diffusion generated in the standard map is introduced using Lévy walk statistics which is based on a generalization of the central-limit theorem and leads to non-Brownian motion. Calculations of the waiting-time distribution of an orbit to stay in a laminar phase and of the distribution of exit times are presented and shown to follow power laws with exponent γ. The propagator P(r, t) obeys a scaled Lévy distribution t−1/γ f(ξ) with f(ξ) ~ exp[−cξ2] for ξ 1 and f(ξ) ~ ξ−1 −γ for ξ 1; ξ = |r|/t1/γ.

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