Lévy statistics in a Hamiltonian system

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Abstract
Enhanced diffusion in a Hamiltonian system is studied in terms of the continuous-time random walk formulation for Lévy walks. The previous Lévy-walk scheme is extended (i) to include interruptions by periods of temporal localization and (ii) to describe motion in two dimensions. We analyze a case of conservative motion in a two-dimensional periodic potential. Numerical calculations of the mean-squared displacements and the propagators for intermediate energies are consistent with the Lévy-walk description.