Abstract
Recent developments have indicated that in addition to out-of-time ordered correlation functions (OTOCs), quantum chaos also has a sharp manifestation in the thermal energy density two-point functions, at least for maximally chaotic systems. The manifestation, referred to as pole-skipping, concerns the analytic behaviour of energy density two-point functions around a special point ω = iλ, k = iλ/vB in the complex frequency and momentum plane. Here λ and vB are the Lyapunov exponent and butterfly velocity characterising quantum chaos. In this paper we provide an argument that the phenomenon of pole-skipping is universal for general finite temperature systems dual to Einstein gravity coupled to matter. In doing so we uncover a surprising universal feature of the linearised Einstein equations around a static black hole geometry. We also study analytically a holographic axion model where all of the features of our general argument as well as the pole-skipping phenomenon can be verified in detail.
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Blake, M., Davison, R.A., Grozdanov, S. et al. Many-body chaos and energy dynamics in holography. J. High Energ. Phys. 2018, 35 (2018). https://doi.org/10.1007/JHEP10(2018)035
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DOI: https://doi.org/10.1007/JHEP10(2018)035