Fast Scramblers Of Small Size

TL;DR

This paper explores the geometrical properties of optical depth in black hole horizons, linking it to fast scrambling and chaos, and examines how small scramblers relate to phase transitions and matrix models in AdS/CFT.

Contribution

It provides a geometric analysis of optical depth as a measure of scrambling, revealing phase transitions and the role of matrix quantum mechanics for small scramblers.

Findings

Optical depth relates to black hole scrambling times.

Phase transitions occur as scramblers become smaller than thermal length.

Small scramblers are described by matrix quantum mechanics.

Abstract

We investigate various geometrical aspects of the notion of `optical depth' in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of the optical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models based on D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.