On the strong anomalous diffusion

الأصل · EN

The superdiffusion behavior, i.e. <x²(t)> t² ν, with ν> 1/2, in general is not completely characherized by a unique exponent. We study some systems exhibiting strong anomalous diffusion, i.e. <|x(t)|q> tq ν⁽q⁾ where ν(2)>1/2 and q ν(q) is not a linear function of q. This feature is different from the weak superdiffusion regime, i.e. ν(q)=const > 1/2, as in random shear flows. The strong anomalous diffusion can be generated by nontrivial chaotic dynamics, e.g. Lagrangian motion in 2d time-dependent incompressible velocity fields, 2d symplectic maps and 1d intermittent maps. Typically the function q ν(q) is piecewise linear. This corresponds to two mechanisms: a weak anomalous diffusion for the typical events and a ballistic transport for the rare excursions. In order to have strong anomalous diffusion one needs a violation of the hypothesis of the central limit theorem, this happens only in a very narrow region of the control parameters space.