Regensburg 2007 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 25: Quantum chaos II

DY 25.5: Vortrag

Donnerstag, 29. März 2007, 10:45–11:00, H2

Leaking Billiards — •Jan Nagler, Moritz Krieger, Marco Linke, Johannes Schönke, and Jan Wiersig — Institut für Theoretische Physik, Universität Bremen, Otto-Hahn-Allee, 28334 Bremen

Billiards are idealizations for systems where particles or waves are confined to cavities, or to other homogeneous regions. In billiard systems a point particle moves freely except for specular reflections from rigid walls. However, billiard walls are not always completely reflective and measurements inside can also open the billiard. Since boundary openings have been studied extensively in the literature, we rather model leakages inside the billiard. In particular, we investigate the classical dynamics of a leakage for a continuous family of billiard systems, that is, the stadium-lemon-billiard family. With a single parameter the geometry of the billiard can be tuned from stadium (being fully hyperbolic) over circle (integrable) to the lemon-shaped billiard (mixed chaotic). For the stadium billiard we found an algebraically decaying mean escape time with the linear size є of the leakage ⟨ n_esc ⟩ ∼ є⁻¹ together which an exponential decay of the survival probability distribution. The finding is nearly independent of the position and size of the leakage, as long as the leakage is much smaller than the system size. Due to the mixed phase space for lemon billiards, the mean escape time depends both on the position and geometry of the leakage. For systems where quasi-regular motion dominates, we found a linear dependence of the mean escape time, ⟨ n_esc ⟩ ∼ 1−є which we refer to as flooding law. Our findings are helpful in understanding dynamics of leaking Hamiltonian systems.