  We suggest the statistical spectral theory of oscillations in quasi-optical
cavity resonator filled with random inhomogeneities. It is shown that
inhomogeneities in the resonator result in intermode scattering leading to the
shift and broadening of spectral lines. The shift and broadening of each line
essentially depends on frequency distance to adjacent spectral lines. With
increasing the distance the influence of inhomogeneities sharply reduces. The
solitary spectral lines which have the distance to the nearest lines quite
large is slightly changed due to small inhomogeneities. Owing to such selective
influence of inhomogeneities on the spectral lines the effective spectrum
rarefaction appears. Both the shift and broadening of spectral lines as well as
spectrum rarefaction in quasi-optical cavity millimeter wave resonator were
detected experimentally. We found out that inhomogeneities result in
stochastization of the resonator spectrum in that mixed state appears, i.e. the
spectrum acquires both regular and random parts. The active self-oscillator
system based on the inhomogeneous quasi-optical cavity millimeter wave
resonator with Gunn diode was studied as well. The inhomogeneous quasi-optical
cavity millimeter wave resonator (passive and active) can serve as a model of
semiconductor quantum billiard. Based on our results we suggest using such
billiards with spectrum rarefied by random inhomogeneities as an active system
of semiconductor laser.
