Enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity.

Abstract

We investigated properties of a singular billiard, that is, a quantum billiard which contains a pointlike (zero-range) perturbation. A singular billiard was simulated experimentally by a rectangular microwave flat resonator coupled to microwave power via wire antennas which act as singular scatterers. The departure from regularity was quantitatively estimated by the short-range plasma model in which the parameter η takes the values 1 and 2 for the Poisson and semi-Poisson statistics, respectively. We show that in the regime of semi-Poisson statistics the experimental power spectrum and the second nearest-neighbor-spacing distribution P(2,s) are in good agreement with their theoretical predictions. Furthermore, the measurement of the two-port scattering matrix allowed us to evaluate experimentally the enhancement factor F(γ^{tot}) in the regime of the semi-Poisson statistics as a function of the total absorption factor γ^{tot}. The experimental results were compared with the analytical formula for F(γ^{tot}) evaluated in this article. The agreement between the experiment and theory is good.