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arXiv · 2605.27512

Many-Body Quantum Chaos At All Time Scales

Antonio M. García-García·Lucas Sá·Jacobus J. M. Verbaarschot·Jie-Ping Zheng
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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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Antonio M. García-García, Lucas Sá, Jacobus J. M. Verbaarschot, Jie-Ping Zheng. 2026-05-26. Many-Body Quantum Chaos At All Time Scales. https://arxiv.org/abs/2605.27512

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