scholarly journals UNIVERSAL CORRELATIONS IN RANDOM MATRICES: QUANTUM CHAOS, THE 1/r2 INTEGRABLE MODEL, AND QUANTUM GRAVITY

1996 ◽  
Vol 11 (15) ◽  
pp. 1201-1219 ◽  
Author(s):  
SANJAY JAIN
Keyword(s):  
Quantum Gravity ◽  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Mathematical Formulation ◽  
Integrable Model ◽  
Moser System

Random matrix theory (RMT) provides a common mathematical formulation of distinct physical questions in three different areas: quantum chaos, the 1-D integrable model with the 1/r2 interaction (the Calogero-Sutherland-Moser system) and 2-D quantum gravity. We review the connection of RMT with these areas. We also discuss the method of loop equations for determining correlation functions in RMT, and smoothed global eigenvalue correlators in the two-matrix model for Gaussian orthogonal, unitary and symplectic ensembles.

scholarly journals Spectral decoupling in many-body quantum chaos

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Jordan Cotler ◽  
Nicholas Hunter-Jones
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Correlation Functions ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Energy Eigenvalue ◽  
Time Dependent ◽  
Late Time ◽  
Many Body ◽  
Many Body Systems

Abstract We argue that in a large class of disordered quantum many-body systems, the late time dynamics of time-dependent correlation functions is captured by random matrix theory, specifically the energy eigenvalue statistics of the corresponding ensemble of disordered Hamiltonians. We find that late time correlation functions approximately factorize into a time-dependent piece, which only depends on spectral statistics of the Hamiltonian ensemble, and a time-independent piece, which only depends on the data of the constituent operators of the correlation function. We call this phenomenon “spectral decoupling”, which signifies a dynamical onset of random matrix theory in correlation functions. A key diagnostic of spectral decoupling is k-invariance, which we refine and study in detail. Particular emphasis is placed on the role of symmetries, and connections between k-invariance, scrambling, and OTOCs. Disordered Pauli spin systems, as well as the SYK model and its variants, provide a rich source of disordered quantum many-body systems with varied symmetries, and we study k-invariance in these models with a combination of analytics and numerics.

scholarly journals Quantum Chaos, Irreversible Classical Dynamics, and Random Matrix Theory

1996 ◽  
Vol 76 (21) ◽  
pp. 3947-3950 ◽  
Author(s):  
A. V. Andreev ◽  
O. Agam ◽  
B. D. Simons ◽  
B. L. Altshuler
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Classical Dynamics

scholarly journals Late time physics of holographic quantum chaos

2021 ◽  
Vol 11 (2) ◽  
Author(s):  
Alexander Altland ◽  
Julian Sonner
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Bound States ◽  
Chaotic Systems ◽  
Matrix Theory ◽  
Effective Field ◽  
Late Time ◽  
Higher Dimensional ◽  
Goldstone Modes

Quantum chaotic systems are often defined via the assertion that their spectral statistics coincides with, or is well approximated by, random matrix theory. In this paper we explain how the universal content of random matrix theory emerges as the consequence of a simple symmetry-breaking principle and its associated Goldstone modes. This allows us to write down an effective-field theory (EFT) description of quantum chaotic systems, which is able to control the level statistics up to an accuracy {O} \left(e^{-S} \right)O(e−S) with SS the entropy. We explain how the EFT description emerges from explicit ensembles, using the example of a matrix model with arbitrary invariant potential, but also when and how it applies to individual quantum systems, without reference to an ensemble. Within AdS/CFT this gives a general framework to express correlations between ``different universes’’ and we explicitly demonstrate the bulk realization of the EFT in minimal string theory where the Goldstone modes are bound states of strings stretching between bulk spectral branes. We discuss the construction of the EFT of quantum chaos also in higher dimensional field theories, as applicable for example for higher-dimensional AdS/CFT dual pairs.

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