Experimental test of a trace formula for two-dimensional dielectric resonators

S. Bittner 1, E. Bogomolny 2, B. Dietz 3, M. Miski-Oglu 3, P. Oria Iriarte 1, A. Richter 1, 4, F. SchÄfer 5

Physical Review E: Statistical, Nonlinear, and Soft Matter Physics 81 (2010) 066215

Resonance spectra of two-dimensional dielectric microwave resonators of circular and square shapes have been measured. The deduced length spectra of periodic orbits were analyzed and a trace formula for dielectric resonators recently proposed by Bogomolny et al. [Phys. Rev. E 78, 056202 (2008)] was tested. The observed deviations between the experimental length spectra and the predictions of the trace formula are attributed to a large number of missing resonances in the measured spectra. We show that by taking into account the systematics of observed and missing resonances the experimental length spectra are fully understood. In particular, a connection between the most long-lived resonances and certain periodic orbits is established experimentally.

  • 1. Institut für Kernphysik,
    Technische Universität Darmstadt
  • 2. Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS),
    CNRS : UMR8626 – Université Paris XI - Paris Sud
  • 3. Institut für Kernphysik,
    Technische Universität Darmstadt
  • 4. ECT, Villa Tombosi,
    Villa Tombosi
  • 5. LENS,
    University of Fiorentino