Moving Mirrors, OTOCs and Scrambling

TL;DR

This paper investigates how moving mirror models in 2D CFTs simulate black hole information dynamics, analyzing OTOCs to distinguish between scrambling and unitary evolution, with implications for understanding quantum chaos and the Page curve.

Contribution

It demonstrates how boundary conditions in moving mirror models influence OTOC behavior, revealing the transition between exponential scrambling and power-law growth in unitary dynamics.

Findings

Maximal chaos occurs for the escaping mirror in large-c CFTs.

Exponential OTOC growth relates to black hole scrambling.

Power-law OTOC growth indicates unitary evolution and Page curve behavior.

Abstract

We explore the physics of scrambling in the moving mirror models, in which a two-dimensional CFT is subjected to a time-dependent boundary condition. It is well-known that by choosing an appropriate mirror profile, one can model quantum aspects of black holes in two-dimensions, ranging from Hawking radiation in an eternal black hole (for an "escaping mirror") to the recent realization of Page curve in evaporating black holes (for a "kink mirror"). We explore a class of OTOCs in the presence of such a boundary and explicitly demonstrate the following primary aspects: First, we show that the dynamical CFT data directly affect an OTOC and maximally chaotic scrambling occurs for the escaping mirror for a large-$c$ CFT with identity block dominance. We further show that the exponential growth of OTOC associated with the physics of scrambling yields a power-law growth in the model for evaporating black holes which demonstrates a unitary dynamics in terms of a Page curve. We also demonstrate that, by tuning a parameter, one can naturally interpolate between an exponential growth associated to scrambling and a power-law growth in unitary dynamics. Our work explicitly exhibits the role of higher-point functions in CFT dynamics as well as the distinction between scrambling and Page curve. We also discuss several future possibilities based on this class of models.