Lévy statistics in a Hamiltonian system

Abstract

Enhanced diffusion in a Hamiltonian system is studied in terms of the continuous-time random walk formulation for L\'evy walks. The previous L\'evy-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 L\'evy-walk description.