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arXiv · 2308.06766

Statistics of local level spacings in single- and many-body quantum chaos

Peng Tian·Roman Riser·Eugene Kanzieper
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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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Peng Tian, Roman Riser, Eugene Kanzieper. 2023-08-13. Statistics of local level spacings in single- and many-body quantum chaos. https://doi.org/10.1103/physrevlett.132.220401

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