in one-dimensional chaotic dynamical systems
Max-Planck-Institut für Physik komplexer Systeme,
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.