Berlin 2015 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 55: Poster - Quantum Systems

DY 55.5: Poster

Donnerstag, 19. März 2015, 16:00–18:00, Poster A

Is the fractal Weyl law valid in partially absorbing systems? — •Moritz Schönwetter and Eduardo G. Altmann — Max-Planck-Institut für Physik komplexer Systeme, Dresden

The fractal Weyl law is a prominent showcase for the nontrivial effect of classical dynamics in a quantum systems. It states that in a chaotic system with an opening the number of long-living quantum states grows with the system size as a power law with a fractional exponent. The exponent is the fractal dimension of the classical invariant set. We study systems in which the opening partially reflects classical trajectories. In this case the fractal dimension of the classical invariant set is equal to the phase-space dimension. Yet, we observe that the number of long-living resonances still scales with a nontrivial exponent. We explain this observation using a statistical procedure that estimates an effective volume available for the resonances. This procedure suggests that in the semiclassical limit the fractal Weyl law is valid with a modified fractal dimension, which cannot be recovered directly from the classical invariant set and its measures.