Missing-level statistics in chaotic microwave networks versus level statistics of partially chaotic systems

Abstract

We present experimental and numerical studies of level statistics in incomplete spectra obtained with fully connected microwave networks simulating quantum chaotic graphs with preserved time reversal symmetry. We demonstrate that, if resonance frequencies are randomly removed from the spectra, the experimental results for the short-range and long-range spectral fluctuations are in good agreement with theoretical predictions of the missing-level statistics for the systems with preserved time reversal symmetry. The same behavior of the short-range spectral fluctuations, e.g., the nearest-neighbor spacing distribution and the integrated nearest-neighbor spacing distribution may be also observed for complete spectra in partially chaotic systems. Using the Rosenzweig-Porter model which interpolates between the chaotic and regular behavior we demonstrate that in a such case the long-range spectral fluctuations differ significantly from the ones predicted by the missing-level statistics.