Experimental and Numerical Study of Spectral Properties of Three-Dimensional Chaotic Microwave Cavities: The Case of Missing Levels

Abstract

We present an experimental and numerical study of missing-level statistics of chaotic threedimensional microwave cavities. The nearest-neighbor spacing distribution, the spectral rigidity, and the power spectrum of level fluctuations were investigated. We show that the theoretical approach to a problem of incomplete spectra does not work well when the incompleteness of the spectra is caused by unresolved resonances. In such a case the fraction of missing levels can be evaluated by calculations based on random matrix theory.