Fine Grained Chaos in AdS_{2} Gravity.

Quantum chaos can be characterized by an exponential growth of the thermal out-of-time-order four-point function up to a scrambling time u[over ^]{*}. 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 two-dimensional anti-de Sitter space (AdS{2}) gravity and the low-energy dynamics of the Sachdev-Ye-Kitaev model. We identify a particular set of 2k-point functions, characterized as being both "maximally braided" and "k-out of time order," which exhibit exponential growth until progressively longer time scales u[over ^]{*}^{(k)}∼(k-1)u[over ^]{*}. 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.