Statistics of Local Level Spacings in Single- and Many-Body Quantum Chaos
Peng Tian1, Roman Riser1,2, Eugene Kanzieper1,3
1School of Mathematical Sciences, Holon Institute of Technology, Holon 5810201, Israel.
Abstract:
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.
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