Chaotic and fractal properties 
of biased deterministic transport

R. Klages

Max-Planck-Institut für Physik komplexer Systeme, Dresden


Second part of the weekly lecture series "Statistical dynamics of nonequilibrium systems" consisting of 5 lectures. Some details of deterministic diffusion in one-dimensional chaotic maps still need to be discussed. In particular, Gaspard's chaotic scattering approach by which transport coefficients can be expressed in terms of dynamical systems quantities will be demonstrated for a simple map. This requires solving the continuity equation of the map via Markov partitions and by constructing topological transition matrices. It may furthermore be sketched how the diffusion coefficient can be computed starting from a Green-Kubo formula, and by evaluating it in terms of fractal functions. Finally, negative and nonlinear response in a chaotic map with a bias will be discussed. The relation of such a map to molecular motors will be illustrated.