scholarly journals Many-Body Quantum Chaos: Analytic Connection to Random Matrix Theory

2018 ◽  
Vol 8 (2) ◽  
Author(s):  
Pavel Kos ◽  
Marko Ljubotina ◽  
Tomaž Prosen
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Chaos ◽  
Matrix Theory ◽  
Many Body

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 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 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

RANDOM MATRIX THEORY AND ITS APPLICATION TO THE DECAY OUT OF A SUPERDEFORMED BAND

2008 ◽  
Vol 17 (supp01) ◽  
pp. 292-303 ◽  
Author(s):  
JIANZHONG GU
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Rapid Development ◽  
Quantum Systems ◽  
Many Body ◽  
Superdeformed Band ◽  
Eigenvalues And Eigenfunctions ◽  
Physical Problems

Originally, random matrix theory (RMT) was designed by Wigner to deal with the statistics of eigenvalues and eigenfunctions of complex many-body quantum systems in 1950s. During the last two decades, the RMT underwent an unexpected and rapid development: The RMT has been successfully applied to an ever increasing variety of physical problems, and it has become an important tool to attack many-body problems. In this contribution I briefly outline the development of the RMT and introduce its basics. Its application to the decay out of a Superdeformed band and a comparison of the approach used in Ref. 34 with that proposed by Vigezzi et al are presented. Current theoretical activities on the decay out problem are reviewed, and the influence of the degree of chaoticity of the normally deformed states on the decay out intensity is examined systematically.

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