Stochastic scattering by random inhomogeneities in SHF oscillatory systems

Nowadays, theoretical and experimental investigations into spectral properties of disordered oscillatory systems assume ever greater importance. It should be noted that most of the first-principle theories were previously developed for open infinite systems, where very important condition of statistical homogeneity of scattering potential was taken to be met with proper accuracy. Theories for oscillatory systems of finite dimensions were developed to much lesser extent, being essentially based on the random matrix theory (RMT) [1]. Meanwhile, it is well known for a long time [2] that RMT-based analysis is applicable, strictly speaking, to systems which are fully chaotic, whereas resonators with inhomogeneous infill should obey hybrid spectra containing both chaotic and regular components. In our recent papers [3,4], novel theoretical methods for studying spectra of disordered oscillating systems were suggested, which are based on direct solution of Helmholtz equation. Also, experimental studies were performed for the purpose of verification of our theoretical forecasts. The basis of our theoretical methods lies in (a) strict separation of oscillation modes in arbitrary random-inhomogeneous wave systems and (b) in the reduction of wave problems stated initially for systems with surface inhomogeneities to the analogous problems for corresponding systems inhomogeneous in the bulk.