Channeling and percolation in two-dimensional chaotic dynamics

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Abstract
The Hamiltonian dynamics of a particle moving in a nearly periodic two-dimensional (2-D) potential of square symmetry is analyzed. The particle undergoes two types of unbounded stochastic or random walks in such a system: a quasi-1-D motion (a ‘‘stochastic channeling’’) and a 2-D motion which results from a sort of stochastic percolation. A scenario for the onset of this stochastic percolation is analyzed. The threshold energy for percolation is found as a function of the perturbation parameter. Each type of random walk has the property of intermittency. The particle transport is anomalous in certain energy intervals.

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