Analyticity constraints bound the decay of the spectral form factor

• URL: http://arxiv.org/abs/2202.11715v3
• Date: Mon, 31 Oct 2022 18:45:05 GMT
• Title: Analyticity constraints bound the decay of the spectral form factor
• Authors: Pablo Martinez-Azcona and Aur\'elia Chenu
• Abstract summary: Quantum chaos cannot develop faster than $lambda leq 2 pi/(hbar beta)$ for systems in thermal equilibrium. We show that similar constraints also bound the decay of the spectral form factor (SFF) The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Quantum chaos cannot develop faster than $\lambda \leq 2 \pi/(\hbar \beta)$ for systems in thermal equilibrium [Maldacena, Shenker & Stanford, JHEP (2016)]. This `MSS bound' on the Lyapunov exponent $\lambda$ is set by the width of the strip on which the regularized out-of-time-order correlator is analytic. We show that similar constraints also bound the decay of the spectral form factor (SFF), that measures spectral correlation and is defined from the Fourier transform of the two-level correlation function. Specifically, the inflection exponent $\eta$, that we introduce to characterize the early-time decay of the SFF, is bounded as $\eta\leq \pi/(2\hbar\beta)$. This bound is universal and exists outside of the chaotic regime. The results are illustrated in systems with regular, chaotic, and tunable dynamics, namely the single-particle harmonic oscillator, the many-particle Calogero-Sutherland model, an ensemble from random matrix theory, and the quantum kicked top. The relation of the derived bound with other known bounds, including quantum speed limits, is discussed.

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