Investigation of the 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 $\eta$ 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.

References in corpus (15)

• Scattering, reflection and impedance of waves in chaotic and disordered systems with absorption
• Quantum and Wave Dynamical Chaos in Superconducting Microwave Billiards
• Are Scattering Properties of Graphs Uniquely Connected to Their Shapes?
• Power spectrum analysis and missing level statistics of microwave graphs with violated time reversal invariance
• Spectral fluctuations and 1/f noise in the order-chaos transition regime
• Experimental investigation of nodal domains in the chaotic microwave rough billiard
• Non-Weyl Microwave Graphs
• Investigation of nodal domains in the chaotic microwave ray-splitting rough billiard
• Chaos and regularity in the doubly magic nucleus 208Pb
• Signatures of a critical point in the many-body localization transition
• Experimental investigation of the elastic enhancement factor in a transient region between regular and chaotic dynamics
• How T-invariance violation leads to an enhanced backscattering with increasing openness of a wave-chaotic system
• Long-range correlations in rectangular cavities containing point-like perturbations
• Elastic enhancement factor as a quantum chaos probe
• Application of topological resonances in experimental investigation of a Fermi golden rule in microwave networks