STOCHASTIC DIFFUSION AND KOLMOGOROV-ENTROPY IN REGULAR AND RANDOM HAMILTONIANS

Abstract

The scalings of the E X B turbulent diffusion coefficient D and the Kolmogorov entropy K with the potential amplitude phi of the fluctuation are studied using the geometrical analysis of closed and extended particle orbits for several types of drift Hamiltonians. The high-amplitude scalings, D is-proportional-to phi2 or phi0 and K is-proportional-to log phi, are shown to arise from different forms of a periodic (four-wave) Hamiltonian phi(xy,t), thereby explaining the controversy in earlier numerical results. For a quasirandom (six-wave) Hamiltonian numerical data for the diffusion D is-proportional-to phi0.92 +/- 0.04 and the Kolmogorov entropy K is-proportional-to phi0.56 +/- 0, 17 are presented and compared with the percolation theory predictions D(p) is-proportional-to phi0.7, K(p) is-proportional-to phi0.5.