Black Holes and Random Matrices
Jordan Cotler,Guy Gur-Ari,Masanori Hanada,Masanori Hanada,Masanori Hanada,Joseph Polchinski,Joseph Polchinski,Phil Saad,Stephen H. Shenker,Douglas Stanford,Alexandre Streicher,Alexandre Streicher,Masaki Tezuka +12 more
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In this paper, the authors show that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems.Abstract:
We argue that the late time behavior of horizon fluctuations in large anti-de Sitter (AdS) black holes is governed by the random matrix dynamics characteristic of quantum chaotic systems. Our main tool is the Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole. We use an analytically continued partition function |Z(β + it)|2 as well as correlation functions as diagnostics. Using numerical techniques we establish random matrix behavior at late times. We determine the early time behavior exactly in a double scaling limit, giving us a plausible estimate for the crossover time to random matrix behavior. We use these ideas to formulate a conjecture about general large AdS black holes, like those dual to 4D super-Yang-Mills theory, giving a provisional estimate of the crossover time. We make some preliminary comments about challenges to understanding the late time dynamics from a bulk point of view.read more
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Entanglement Wedge Reconstruction and the Information Paradox
TL;DR: In this paper, it was shown that there is a phase transition in the location of the quantum Ryu-Takayanagi surface, at precisely the Page time, at an infalling time approximately the scrambling time β/2πlogSBH into the past.
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The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual
TL;DR: In this paper, a non-local correction to the Schwarzian effective action is found by integrating out the bulk degrees of freedom in a certain variant of dilaton gravity, and general properties of out-of-time-order correlators are discussed.
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Replica wormholes and the black hole interior
TL;DR: In this paper, the Page transition of an evaporating black hole from holographic computations of entanglement entropy has been obtained using the replica trick, from geometries with a spacetime wormhole connecting the different replicas.
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JT gravity as a matrix integral
TL;DR: In this paper, the authors present exact results for partition functions of JT gravity on two-dimensional surfaces of arbitrary genus with an arbitrary number of boundaries, and show that the partition functions correspond to the genus expansion of a certain matrix integral.
Journal ArticleDOI
Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography
Richard A. Davison,Wenbo Fu,Antoine Georges,Antoine Georges,Antoine Georges,Yingfei Gu,Kristan Jensen,Subir Sachdev,Subir Sachdev +8 more
TL;DR: In this article, the thermodynamic properties of the Sachdev-Ye-Kitaev (SYK) models of fermions with a conserved fermion number Q were investigated.
References
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Chaos and quantum thermalization
TL;DR: It is shown that a bounded, isolated quantum system of many particles in a specific initial state will approach thermal equilibrium if the energy eigenfunctions which are superposed to form that state obey Berry's conjecture, and argued that these results constitute a sound foundation for quantum statistical mechanics.
Journal ArticleDOI
Quantum statistical mechanics in a closed system
TL;DR: A closed quantum-mechanical system with a large number of degrees of freedom does not necessarily give time averages in agreement with the microcanonical distribution, so by adding a finite but very small perturbation in the form of a random matrix, the results of quantum statistical mechanics are recovered.
Journal ArticleDOI
A bound on chaos
TL;DR: In this paper, a sharp bound on the rate of growth of chaos in thermal quantum systems with a large number of degrees of freedom is given, based on plausible physical assumptions, establishing this conjecture.
Journal ArticleDOI
Remarks on the Sachdev-Ye-Kitaev model
Juan Maldacena,Douglas Stanford +1 more
TL;DR: In this paper, the authors studied the quantum mechanical model of $N$ Majorana fermions with random interactions of a few Fermions at a time (Sachdev-Ye-Kitaev model) in the large N$ limit.
Journal ArticleDOI
Statistical Theory of the Energy Levels of Complex Systems. I
TL;DR: In this article, three kinds of statistical ensembles are defined, representing a mathematical idealization of the notion of ''all physical systems with equal probability'' and three groups are studied in detail, based mathematically upon the orthogonal, unitary and symplectic groups.
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