# Out-of-time-order correlator As the name suggests, an **out-of-time-order correlator** (OTOC) is a correlator that is not ordered chronologically. An example is $\langle O(t_1)O(t_2)O(t_3)\rangle$ where $t_2>t_1>t_3$. A commonly studied OTOC is $\langle V(x,t) W(0,0) V(x,t) W(0,0)\rangle$, where $V$ and $W$ are two localised operators. This is often useful as a diagnosis of [[0008 Quantum chaos|quantum chaos]], where it is used to define the [[0466 Lyapunov exponent|Lyapunov exponent]] and the [[0167 Butterfly velocity|butterfly velocity]]. In the literature, when people say "the OTOC" without further specifications, they usually mean this one. In [[0001 AdS-CFT|AdS/CFT]], the corresponding bulk process dual to the OTOC is the scattering of highly boosted particles near the black hole's horizon. Its classical limit is described by a [[0117 Shockwave|shockwave]]. ## Refs - review - [[2022#Xu, Swingle (Review)]] ## Extensions - replica OTOC: - [[Trunin2023long]][](https://arxiv.org/pdf/2308.02392.pdf) and [[Trunin2023short]][](https://arxiv.org/pdf/2308.02403.pdf) - OTOC as asymptotic observable in QFT - [[2023#Caron-Huot, Giroux, Hannesdottir, Mizera (Aug)]]