Test of Trace Formulas for Spectra of Superconducting Microwave Billiards

Rudi Schäfer, Ulrich Kuhl, Michael Barth +1 more

Ulrich Kuhl, Emil Persson, Michael Barth +1 more

S. Sridhar, Daniel O. Hogenboom, Balam A. Willemsen

Srinivas Sridhar

C. Dembowski, H.-D. Gräf, A. Heine +3 more

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.

C. Dembowski, Barbara Dietz, H.-D. Gräf +4 more

Trace formulas provide a direct relation between the eigenvalues of a given quantum system and the properties of the periodic orbits of its classical counterpart. About 25 years ago, Balian and Duplantier derived a trace formula for the resonance density of three-dimensional chaotic microwave cavities. We will present the first experimental test of this semiclassical approximation performed with a microwave cavity of the shape of a three-dimensional Bunimovich billiard.