Fine-Grained Chaos in $AdS_2$ Gravity

TL;DR

This paper explores how higher-point correlation functions in $AdS_2$ gravity and the SYK model exhibit exponential growth over longer timescales, revealing a hierarchy in quantum information scrambling.

Contribution

It introduces a class of maximally braided, k-OTO $2k$-point functions in the Schwarzian theory that grow exponentially until longer times, extending chaos characterization.

Findings

Higher-point functions grow exponentially up to longer timescales

Identifies a hierarchy of scrambling times for different correlation functions

Provides a new perspective on quantum information scrambling in $AdS_2$ gravity

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.