Analytical all-time expressions for Green's and OTOC functions in 4-body SYK model show early exponential growth then decay, followed by late-time dip-ramp-plateau patterns deviating from ergodic predictions due to local energy correlations for N mod 8 = 2,6.
Chaos in the black hole S-matrix
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abstract
Recent work by Shenker, Stanford, and Kitaev has related the black hole horizon geometry to chaotic behavior. We extend this from eternal black holes to black holes that form and then evaporate. This leads to an identity for the change in the black hole S-matrix (over times shorter than the scrambling time) due an addition infalling particle, elaborating an idea of 't Hooft.
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Photon rings around black holes saturate the quantum chaos bound via Lyapunov exponents of null geodesics and OTOCs in the near-ring region.
In the fully chaotic regime of the kicked top, long-time freeness is reached exponentially fast, accompanied by a hierarchy of time scales indicating a multifractal approach.
This review surveys the Loschmidt echo, OTOCs, and Krylov complexity as quantum proxies for classical Lyapunov exponents in chaotic systems.
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Quantum analogues of exponential sensitivity: from Loschmidt echo to Krylov complexity
This review surveys the Loschmidt echo, OTOCs, and Krylov complexity as quantum proxies for classical Lyapunov exponents in chaotic systems.