Investigation of the enhancement factor in the regime of semi-Poisson statistics in a singular microwave cavity

TL;DR

This study experimentally investigates a singular microwave cavity exhibiting semi-Poisson statistics, measuring spectral properties and enhancement factors, and finds good agreement with theoretical models for semi-Poisson behavior.

Contribution

The paper provides the first experimental measurement of the enhancement factor in a semi-Poisson regime within a singular microwave cavity, validating theoretical predictions.

Findings

Power spectrum matches semi-Poisson predictions.

Second nearest-neighbor spacing distribution aligns with theory.

Enhancement factor measurements agree with analytical formula.

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 $\eta$ 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 $F(\gamma^{tot})$ in the regime of the semi-Poisson statistics as a function of the total absorption factor $\gamma^{tot}$. The experimental results were compared with the analytical formula for $F(\gamma^{tot})$ evaluated in this article. The agreement between the experiment and theory is good.