Crossover between Ballistic and Normal Diffusion

Abstract

Crossover between ballistic motion and normal diffusion is studied based on the continuous-time random walk (CTRW) approach in order to analyze universal properties of strongly correlated motion and the decay process of correlation in deterministic diffusion. There exists a characteristic time scale τ. For the time region t ≪τ, ballistic motion is observed, which is followed by normal diffusion for t ≫τ. Higher-order moments are analytically obtained, and it is found that they obey scaling relations that are reminiscent of the generalized extended self-similarity (GESS) found in turbulent systems. As a simple dynamical system for numerical simulations, the climbing sine map in the vicinity of band crisis is considered. Good agreement between the theory and the numerical simulations is observed.