Volume 118, Number 3, May 2017
|Number of page(s)||7|
|Published online||13 July 2017|
Exceptional points in the elliptical three-disk scatterer using semiclassical periodic orbit quantization
Institut für Theoretische Physik, Universität Stuttgart - 70550 Stuttgart, Germany
Received: 26 April 2017
Accepted: 20 June 2017
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 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 symmetry is preserved. The two-dimensional parameter plane of the system is then spanned by the distance between and the excentricity of the elliptical disks. As typical signatures of exceptional points we observe the permutation of two resonances when an exceptional point is encircled in parameter space, and a non-Lorentzian resonance line shape in the weighted density of states.
PACS: 05.45.Mt – Quantum chaos; semiclassical methods / 03.65.Sq – Semiclassical theories and applications / 05.45.Pq – Numerical simulations of chaotic systems
© EPLA, 2017
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