Berlin 2012 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 29: Posters II
DY 29.4: Poster
Donnerstag, 29. März 2012, 17:00–19:00, Poster A
Integrable Approximation for Regular Regions Using the Optimized Canonical Transformation Method — Arnd Bäcker1,2, Roland Ketzmerick1,2, •Clemens Löbner1,2, and Steffen Löck1 — 1Technische Universität Dresden, Institut für Theoretische Physik, 01062 Dresden — 2MPI für Physik komplexer Systeme, 01187 Dresden
Our aim is to approximate the dynamics of a regular island in a non-integrable Hamiltonian H by an integrable Hamiltonian Hreg. For this purpose we introduce optimized canonical transformations in phase space such that the regular dynamics of H and Hreg agree as closely as possible.
We apply this optimized 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.