Many-Body Quantum Chaos At All Time Scales

• URL: http://arxiv.org/abs/2605.27512v1
• Date: Tue, 26 May 2026 18:00:03 GMT
• Title: Many-Body Quantum Chaos At All Time Scales
• Abstract summary: We study the Green's and out-of-time order correlation functions of the four-body, $N$-Majorana Sachdev-Ye-Kitaev model.<n>For late times that scale exponentially with $N$, both functions have a dip-ramp-plateau pattern for $N mathrmmod8 = 2, 6$ that deviates substantially from the ergodic prediction.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We describe the dynamics of many-body quantum chaotic systems at all time scales by studying the Green's and out-of-time order correlation (OTOC) functions of the four-body, $N$-Majorana Sachdev-Ye-Kitaev model. By combining the scramblon formalism and random-matrix-theory techniques, we obtain analytical expressions for these functions at all times. The early exponential growth of the OTOC is followed by an exponential decay at a rate governed by that of the Green's function (the real part of the leading complex Ruelle-Pollicott resonances). For late times that scale exponentially with $N$, both functions have a dip-ramp-plateau pattern for $N \mathrm{mod}8 = 2, 6$ that deviates substantially from the ergodic prediction due to local-in-energy correlations of matrix elements and eigenvalues, even after the Heisenberg time.

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