FAST AND SLOW PROCESSES IN ANOMALOUS DIFFUSION

Abstract

Using a toy model of anomalous diffusion (for which probability distribution P(r, t) is available in analytic form), it is shown that separation between fast and slow processes in anomalous diffusion using rescaling ζ=r/<r2(t)>1/2 in the probability distribution can lead to a pseudo-asymptotic effect. This effect implies that in considerably long intervals of time, the probability distribution P(ζ,t), effectively, depends only on ζ. Moreover, in these intervals, P(ζ) can be fitted by stretched exponential representation P(ζ)~ exp -[cζγ], where exponent γ is different from real large time asymptotic γ∞. Actually, the exponent γ depends on time and, very slowly, approaches the asymptotic value γ∞ with increasing time.