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 two-dimensional anti–de Sitter space (${\mathrm{AdS}}_2$) 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 ${\widehat{u}}_{*}^{(k)}\sim (k-1){\widehat{u}}_{*}$. 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.

中文翻译：

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AdS2重力中的细粒度混沌

量子混沌的特征在于热失序四点函数在加扰时间之前呈指数增长 ${\widehat{ü}}_{*}$。我们讨论了某些较高点相关函数的该语句的概括。具体而言，我们研究了一维时间重新参数化模式的Schwarzian理论，该模型描述了二维反de Sitter空间（${\mathrm{广告}}_{\mathrm{2个}}$重力和Sachdev-Ye-Kitaev模型的低能动力学。我们确定一组特定的$\mathrm{2个}ķ$点功能，具有“最大编织”和“$ķ$-按时间顺序排列”，直到逐渐变长的时间范围内为止，都会呈指数增长 ${\widehat{ü}}_{*}^{（ķ）}〜（ķ-\mathrm{1个}）{\widehat{ü}}_{*}$。我们建议将这种解释解释为对越来越精细的量子信息度量的争夺，这相应地需要更长的时间才能逐渐达到其热值。