Renormalization group theory of anomalous transport in systems with Hamiltonian chaos

Abstract

We present a general scheme to describe particle kinetics in the case of incomplete Hamiltonian chaos when a set of islands of stability forms a complicated fractal space-time dynamics and when there is orbit stickiness to the islands’ boundary. This kinetics is alternative to the ‘‘normal’’ Fokker–Planck–Kolmogorov equation. A new kinetic equation describes random wandering in the fractal space-time. Critical exponents of the anomalous kinetics are expressed through dynamical characteristics of a Hamiltonian using the renormalization group approach. Renormalization transformation has been applied simultaneously for space and time and fractional calculus has been exploited.