Exceptional points in the elliptical threedisk scatterer using semiclassical periodic orbit quantization
Abstract
The threedisk 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 nonHermitian 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 threedisk 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 C_{3{v}} symmetry is preserved. The twodimensional 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 nonLorentzian resonance line shape in the weighted density of states.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 May 2017
 DOI:
 10.1209/02955075/118/30006
 arXiv:
 arXiv:1705.00197
 Bibcode:
 2017EL....11830006L
 Keywords:

 Nonlinear Sciences  Chaotic Dynamics;
 Quantum Physics
 EPrint:
 7 pages, 7 figures, 1 table