Quantum chaos inside space-temporal Sinai billiards

TL;DR

This paper explores quantum chaos phenomena in space-temporal Sinai billiards, analyzing scattering, trapped orbits, and survival probabilities in a semiclassical framework, with implications for relativistic quantum field theory.

Contribution

It introduces the concept of space-temporal Sinai billiards and derives general expressions for survival probabilities and scattering delays in the semiclassical regime.

Findings

Unavoidable formation of trapped semiclassical orbits

Derived expressions for survival probabilities and scattering delays

Discussion on extensions to relativistic quantum field theory

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.