  We discuss general aspects of non-relativistic quantum chaos theory of
scattering of a quantum particle on a system of a large number of naked
singularities. We define such a system space-temporal Sinai billiard We dis-
cuss the problem in semiclassical approach. We show that in semiclassical
regime the formation of trapped periodic semiclassical orbits inside the sys-
tem is unavoidable. This leads to general expression of survival probabilities
and scattering time delays, expanded to the chaotic Pollicott-Ruelle reso-
nances. Finally, we comment on possible generalizations of these aspects to
relativistic quantum field theory.
