Stochastic dynamics from the fractional Fokker-Planck-Kolmogorov equation:Large-scale behavior of the turbulent transport coefficient - art. no. 047301

The formulation of the fractional Fokker-Planck-Kolmogorov (FPK) equation [ Physica D 76, 110 (1994)] has led to important advances in the description of the stochastic dynamics of Hamiltonian systems. Here, the long-time beha vior of the basic transport processes obeying the fractional FPK equation i s analyzed. A derivation of the large-scale turbulent transport coefficient for a Hamiltonian system with 1 1/2 degrees of freedom is proposed in conn ection with the fractal structure of the particle chaotic trajectories. The principal transport regimes (i.e., a diffusion-type process, ballistic mot ion, subdiffusion in the limit of the frozen Hamiltonian, and behavior asso ciated with self-organized criticality) are obtained as partial cases of th e generalized transport law. A comparison with recent numerical and experim ental studies is given.