Dresden 2011 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 37: Quantum Chaos II
DY 37.4: Talk
Thursday, March 17, 2011, 16:45–17:00, ZEU 118
Fractal Weyl law for three-dimensional chaotic hard-sphere scattering systems — •Alexander Eberspächer1, Jörg Main2, and Günter Wunner2 — 1Institut für Theoretische Physik, Otto-von-Guericke Universität, 39016 Magdeburg, Germany — 2Institut für Theoretische Physik 1, Universität Stuttgart, 70550 Stuttgart, Germany
The fractal Weyl law [1] connects the asymptotic level number with the fractal dimension of the chaotic repeller. We provide the first test for the fractal Weyl law for a three-dimensional open scattering system.
For the four-sphere billiard, we investigate the chaotic repeller and discuss the semiclassical quantization of the system by the method of cycle expansion with symmetry decomposition. We test the fractal Weyl law for various symmetry subspaces and sphere-to-sphere separations [2].
[1] W. T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003).
[2] A. Eberspächer, J. Main, G. Wunner, Phys. Rev. E 82, 046201 (2010)