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arXiv · 1712.04963

Fine-Grained Chaos in $AdS_2$ Gravity

Felix M. Haehl·Moshe Rozali
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Abstract

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time $\widehat{u}_*$. We discuss generalizations of this statement for certain higher-point correlation functions. For concreteness, we study the Schwarzian theory of a one-dimensional time reparametrization mode, which describes $AdS_2$ gravity and the low-energy dynamics of the SYK model. We identify a particular set of $2k$-point functions, characterized as being both "maximally braided" and "k-OTO", which exhibit exponential growth until progressively longer timescales $\widehat{u}^{(k)}_* = (k-1)\widehat{u}_*$. We suggest an interpretation as scrambling of increasingly fine-grained measures of quantum information, which correspondingly take progressively longer time to reach their thermal values.

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BibTeXRIS

Felix M. Haehl, Moshe Rozali. 2017-12-13. Fine-Grained Chaos in $AdS_2$ Gravity. https://doi.org/10.1103/physrevlett.120.121601

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