Fast Scramblers Of Small Size

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.

14 pages, 3 figures. Added references

References in corpus (4)

• Black holes as mirrors: quantum information in random subsystems
• The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
• A Matrix Model for Black Hole Thermalization
• Deconstructing the Little Hagedorn Holography

Cited by in corpus (10)

• Universality in Chaos of Particle Motion near Black Hole Horizon
• Large N classical dynamics of holographic matrix models
• On operator growth and emergent Poincaré symmetries
• Black holes as random particles: entanglement dynamics in infinite range and matrix models
• Geometry And Quantum Noise
• Fast Scramblers, Horizons and Expander Graphs
• De Finetti theorems and entanglement in large-N theories and gravity
• Causality bounds chaos in geodesic motions
• The quantum cat map on the modular discretization of extremal black hole horizons
• Fast Scramblers And Ultrametric Black Hole Horizons