Regensburg 2013 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 33: Poster II
DY 33.54: Poster
Donnerstag, 14. März 2013, 17:00–19:00, Poster C
Integrable Approximation of Regular Islands: The Iterative Canonical Transformation Method — •Clemens Löbner1,2, Steffen Löck1,3, Arnd Bäcker1,2, and Roland Ketzmerick1,2 — 1Technische Universität Dresden, Institut für Theoretische Physik, 01062 Dresden — 2MPI für Physik komplexer Systeme, 01187 Dresden — 3Technische Universität Dresden, OncoRay - National Center for Radiation Research in Oncology, 01307 Dresden
Our aim is to approximate the dynamics of a regular island in a non-integrable Hamiltonian H by an integrable Hamiltonian Hreg. We present a new method which allows to find Hreg for arbitrarily many degrees of freedom. The method is based on the construction of an integrable approximation in action representation which is then improved in phase-space representation by iterative applications of canonical transformations. These transformations are optimized such that the regular dynamics of H and Hreg agree as closely as possible.
We apply this iterative canonical transformation method to the standard map and the cosine billiard. In the second case the resulting integrable Hamiltonian describes a billiard with the same boundary, but a nontrivial time evolution. This provides a basis for the future determination of regular-to-chaotic tunneling rates for generic billiards with the fictitious integrable system approach.