Chaotic Fast Scrambling At Black Holes
arXiv:1105.2581 · doi:10.1103/PhysRevD.84.106012
Abstract
Fast scramblers process information in characteristic times scaling logarithmically with the entropy, a behavior which has been conjectured for black hole horizons. In this note we use the AdS/CFT fold to argue that causality bounds on information flow only depend on the properties of a single thermal cell, and admit a geometrical interpretation in terms of the optical depth, i.e. the thickness of the Rindler region in the so-called optical metric. The spatial sections of the optical metric are well approximated by constant-curvature hyperboloids. We use this fact to propose an effective kinetic model of scrambling which can be assimilated to a compact hyperbolic billiard, furnishing a classic example of hard chaos. It is suggested that classical chaos at large N is a crucial ingredient in reconciling the notion of fast scrambling with the required saturation of causality.
10 pages, 2 figures
References in corpus (14)
- Black holes as mirrors: quantum information in random subsystems
- Holography from Conformal Field Theory
- Thermalization of Strongly Coupled Field Theories
- Holographic Evolution of Entanglement Entropy
- Chaos Rules out Integrability of Strings in AdS_5 x T^{1,1}
- Chaos in the Gauge/Gravity Correspondence
- The arrow of time, black holes, and quantum mixing of large N Yang-Mills theories
- Evidence for fast thermalization in the plane-wave matrix model
- A Matrix Model for Black Hole Thermalization
- Typicality versus thermality: An analytic distinction
- Addendum to Fast Scramblers
- Quantum geometry and gravitational entropy
- Universal properties of the near-horizon optical geometry
- Quantitative approaches to information recovery from black holes
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- Jerusalem Lectures on Black Holes and Quantum Information
- Towards the fast scrambling conjecture
- Entanglement Entropy from a Holographic Viewpoint
- Universality in Chaos of Particle Motion near Black Hole Horizon
- Black holes, complexity and quantum chaos
- Scrambling in the Black Hole Portrait
- Krylov complexity and orthogonal polynomials
- Dynamics and Transport at the Threshold of Many-Body Localization
- Extreme Decoherence and Quantum Chaos
- Large N classical dynamics of holographic matrix models
- Looking for (and not finding) a bulk brane
- Black holes as random particles: entanglement dynamics in infinite range and matrix models
- Backdraft: String Creation in an Old Schwarzschild Black Hole
- Scrambling with Matrix Black Holes
- De Finetti theorems and entanglement in large-N theories and gravity
- Causality bounds chaos in geodesic motions
- Simple analog of the black-hole information paradox in quantum Hall interfaces
- Quasinormal modes of BTZ black hole and Hawking-like radiation in graphene
- Complexity is not Enough for Randomness
- Dissipative Nonlinear Dynamics in Holography
- Chaotic Information Processing by Extremal Black Holes
- Fast Scramblers, Democratic Walks and Information Fields