# Regensburg 2013 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 30: Quantum Chaos II

### DY 30.5: Vortrag

### Donnerstag, 14. März 2013, 16:00–16:15, H47

**On the fractal dimension spectrum of open chaotic systems** — •Moritz Schönwetter^{1}, Orestis Georgiou^{2}, and Eduardo Altmann^{1} — ^{1}MPIPKS, Dresden — ^{2}Toshiba 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).