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Chaotic and fractal properties

of biased deterministic transport

**R. Klages**
Max-Planck-Institut für Physik komplexer Systeme,
Dresden

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Abstract:

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.