Rectangular microwave resonators with magnetic anisotropy. Mapping onto pseudo integrable rhombus

The rectangular microwave resonator filed by a ferrite with uniaxial magnetic anisotropy is considered. It is shown that this task can be reduced to an empty rhombus resonator with vertex angle defined by external magnetic field provided the magnetic anisotropy of the ferrite is strong. Therefore statistics of eigen frequencies for TM modes is described by the Brody or semi-Poisson distribution with some exceptional cases.