Date: December 1995
Creator: Floriani, Elena; Grigolini, Paolo & Mannella, Riccardo
Description: This article discusses noise-induced transition from anomalous to ordinary diffusion and the crossover time as a function of noise intensity. Abstract: We study the interplay between a deterministic process of weak chaos, responsible for the anomalous diffusion of a variable x, and a white noise of intensity ≡. The deterministic process of anomalous diffusion results from the correlated fluctuations of a statistical variable ξ between two distinct values +1 and -1, each of them characterized by the same waiting time distribution ψ(t), given by ψ(t)≃ t(-μ) with 2 < μ < 3, in the long-time limit. We prove that under the influence of a weak white noise of intensity ≡, the process of anomalous diffusion becomes normal at a time t(c) given by t(c) ~ 1/≡(β)(μ). Here β(μ) is a function of μ which depends on the dynamical generator of the waiting-time distribution ψ(t). We derive an explicit expression for β(μ) in the case of two dynamical systems, a one-dimensional superdiffusive map and the standard map in the accelerating state. The theoretical prediction is supported by numerical calculations.
Contributing Partner: UNT College of Arts and Sciences