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2017

Fine-Grained Chaos in $AdS_2$ Gravity

Haehl, Felix M., Rozali, Moshe

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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 $\widehat{u}^{(k)}_* = (k-1)\widehat{u}_*$.

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