First Experimental Test of a Trace Formula for Billiard Systems Showing Mixed Dynamics

C. Dembowski, H.-D. Gräf, A. Heine, T. Hesse, H. Rehfeld, and A. Richter
Phys. Rev. Lett. 86, 3284 – Published 9 April 2001
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Abstract

In general, trace formulas relate the density of states for a given quantum mechanical system to the properties of the periodic orbits of its classical counterpart. Here we report for the first time on a semiclassical description of microwave spectra taken from superconducting billiards of the Limaçon family showing mixed dynamics in terms of a generalized trace formula derived by Ullmo et al. [Phys. Rev. E 54, 136 (1996)]. This expression not only describes mixed-typed behavior but also the limiting cases of fully regular and fully chaotic systems and thus presents a continuous interpolation between the Berry-Tabor and Gutzwiller formulas.

  • Received 17 August 2000

DOI:https://doi.org/10.1103/PhysRevLett.86.3284

©2001 American Physical Society

Authors & Affiliations

C. Dembowski1, H.-D. Gräf1, A. Heine1, T. Hesse2, H. Rehfeld1, and A. Richter1

  • 1Institut für Kernphysik, Technische Universität Darmstadt, D-64289 Darmstadt, Germany
  • 2Abteilung Theoretische Physik, Universität Ulm, D-89069 Ulm, Germany

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Vol. 86, Iss. 15 — 9 April 2001

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