Deterministic diffusion 
in one-dimensional chaotic dynamical systems

R. Klages

Max-Planck-Institut für Physik komplexer Systeme, Dresden


This will be the first part of the weekly lecture series "Statistical dynamics of nonequilibrium systems" consisting of 5 lectures. I will start by discussing deterministic diffusion in one-dimensional periodic arrays of scatterers defined by piecewise linear maps. I will discuss three different approaches to compute the parameter-dependent diffusion coefficient of such models:
1. on the basis of a simple random walk on the line
2. solving the continuity equation of the deterministic map via Markov partitions and by constructing topological transition matrices. Gaspard's approach, by which he expresses transport coefficients in terms of dynamical systems quantities, will be discussed.
3. the diffusion coefficient is computed by starting from a Green-Kubo formula, and by evaluating it it terms of fractal functions
Some basic knowledge of dynamical systems theory might be helpful.