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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 Bäcker^1,2, Roland Ketzmerick^1,2, •Clemens Löbner^1,2, 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 H_reg. For this purpose we introduce optimized canonical transformations in phase space such that the regular dynamics of H and H_reg 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.