A Matrix Model for Black Hole Thermalization

Abstract

We present a matrix model which is intended as a toy model of the gauge dual of an AdS black hole. In particular, it captures the key property that at infinite $N$ correlators decay to zero on long time scales, while at finite $N$ this cannot happen. The model consists of a harmonic oscillator in the adjoint which acts as a heat bath for a particle in the fundamental representation. The Schwinger-Dyson equation reduces to a closed recursion relation, which we study by various analytical and numerical methods. We discuss some implications for the information problem.

23 pages, 5 eps figures. v2: expanded discussion of model, added references. v3: slightly expanded conclusions

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• Black Hole Collapse in the 1/c Expansion
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• 2D CFT Partition Functions at Late Times
• Chaos in the black hole S-matrix
• Random free fermions: An analytical example of eigenstate thermalization
• Black Holes, AdS, and CFTs
• Measuring Black Hole Formations by Entanglement Entropy via Coarse-Graining
• Spin Matrix Theory: A quantum mechanical model of the AdS/CFT correspondence
• Matrix Models for the Black Hole Information Paradox
• Phases of scrambling in eigenstates
• Large N classical dynamics of holographic matrix models
• Schur-Weyl duality as an instrument of Gauge-String duality
• Evolution of entanglement entropy in the D1-D5 brane system
• Quantitative approaches to information recovery from black holes
• Correlators in W_N Minimal Model Revisited
• Black holes as random particles: entanglement dynamics in infinite range and matrix models
• Quantum chaos, thermalization and entanglement generation in real-time simulations of the BFSS matrix model
• Chaotic Fast Scrambling At Black Holes
• Non-equilibrium Dynamics of O(N) Nonlinear Sigma models: a Large-N approach
• Fast Scramblers, Horizons and Expander Graphs
• Extended Eigenstate Thermalization and the role of FZZT branes in the Schwarzian theory
• Dynamical tachyons on fuzzy spheres
• De Finetti theorems and entanglement in large-N theories and gravity
• Tensor Models for Black Hole Probes
• Fast Scramblers Of Small Size
• Black Hole Formation at the Correspondence Point
• Scrambling in Yang-Mills
• Interactions resolve state-dependence in a toy-model of AdS black holes
• Quantum Black Hole Formation in the BFSS Matrix Model
• Four-point function in the IOP matrix model
• Brick Walls for Black Holes in AdS/CFT
• A Strategy for Proving the Strong Eigenstate Thermalization Hypothesis : Chaotic Systems and Holography
• Black Hole Horizons and Bose-Einstein Condensation
• Non-adiabaticity and improved back-reaction
• A simple model for Hawking radiation
• Non-equilibrium Wilson loops in N=4 SYM
• Homolumo Gap from Dynamical Energy Levels
• Conformal Quivers and Melting Molecules
• Time-dependent Backgrounds in String Theory and Dualities
• Dynamical and Quenched Random Matrices and Homolumo Gap