Quantum chaos inside space-temporal Sinai billiards

Abstract

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.

Version accepted in Int. J. of Geometric Methods in Modern Physics. arXiv admin note: substantial text overlap with arXiv:1508.04054, arXiv:1510.09128

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