Statistics of Local Level Spacings in Single- and Many-Body Quantum Chaos.

We introduce a notion of local level spacings and study their statistics within a random-matrix-theory approach. In the limit of infinite-dimensional random matrices, we determine universal sequences of mean local spacings and of their ratios which uniquely identify the global symmetries of a quantum system and its internal-chaotic or regular-dynamics. These findings, which offer a new framework to monitor single- and many-body quantum systems, are corroborated by numerical experiments performed for zeros of the Riemann zeta function, spectra of irrational rectangular billiards, and many-body spectra of the Sachdev-Ye-Kitaev Hamiltonians.