Dresden 2017 – scientific programme
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DY: Fachverband Dynamik und Statistische Physik
DY 32: Quantum Chaos
DY 32.3: Talk
Wednesday, March 22, 2017, 10:30–10:45, HÜL 186
Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization — •Niklas Liebermann, Jörg Main, and Günter Wunner — 1. Institut für Theoretische Physik, Universität Stuttgart, Germany
The three-disk scatterer has served as a paradigm for semiclassical periodic orbit quantization of classical chaotic systems using Gutzwiller’s trace formula. It represents an open quantum system, thus leading to spectra of complex eigenenergies. An interesting general feature of open quantum systems described by non-Hermitian operators is the possible existence of exceptional points where not only the complex eigenvalues but also their respective eigenvectors coincide.
Using Gutzwiller’s periodic orbit theory we show that exceptional points exist in a three-disk scatterer as well if the system’s geometry is modified by extending the system from circular to elliptical disks. The extension is implemented in such a way that the system’s characteristic C3v symmetry is conserved. The two-dimensional parameter plane of the system is then spanned by the distance and the excentricity of the elliptical disks. As characteristic features of exceptional points we observe the permutation of two resonances when an exceptional point is encircled in parameter space and the non-exponential decay of the periodic orbit signal. This non-exponential behaviour is related to a non-Lorentzian shape of resonances in the density of states.