Regensburg 2010 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Posters II

DY 30.25: Poster

Thursday, March 25, 2010, 16:00–18:00, Poster C

Using extreme value theory to determine transport statistics of a disordered Hamiltonian system — •Ines Hartwig and Günter Radons — TU Chemnitz, Germany

We combine the treatment of deterministic chaos in Hamiltonian systems with aspects of the theory of disordered systems for a simple two-dimensional twist map.

Motivated by applications from plasma turbulence, we replace the cosine potential of the well-known Chirikov-Taylor standard map by random one-dimensional analytic potentials with spatial disorder but periodic boundaries.

Structures in phase space include nested island hierarchies, chaotic seas and invariant tori. But while each disorder realization has its specific KAM behavior, the ensemble of systems has to be treated statistically. A fundamental domain of controllable size in phase space enables us to investigate the limit of a disordered system of infinite size using extreme value theory. We obtain distributions of critical perturbation amplitudes, which in turn allow us to conclude about transport exponents and fractions of particles actually contributing to unbounded motion.