Regensburg 2013 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 30: Quantum Chaos II

DY 30.5: Talk

Thursday, March 14, 2013, 16:00–16:15, H47

On the fractal dimension spectrum of open chaotic systems — •Moritz Schönwetter¹, Orestis Georgiou², and Eduardo Altmann¹ — ¹MPIPKS, Dresden — ²Toshiba Research Europe Limited, Bristol, England

Wave and quantum properties of open systems are nowadays understood in terms of the invariant sets of their classically chaotic counterparts as for example in the fractal Weyl law connecting the asymptotic resonance density with the fractal dimension of the classical repeller. In this talk we introduce an efficient and accurate algorithm to numerically compute the full spectrum of Renyi-dimensions (D_q), and use it to investigate physically relevant classes of Hamiltonian systems exhibiting interesting D_q: (i) systems with a non-hyperbolic component, in which case we argue that the dimensions should be considered scale-dependent and the dynamics characterized by effective dimensions; and (ii) open systems in which trajectories are only partially reflected in a region of the boundary and which exhibit a non-constant D_q spectrum (multifractals).