scholarly journals A MODEL OF TWO-DIMENSIONAL TURBULENCE USING RANDOM MATRIX THEORY

2002 ◽  
Vol 17 (23) ◽  
pp. 1539-1550 ◽  
Author(s):  
SAVITRI V. IYER ◽  
S. G. RAJEEV
Keyword(s):  
Maximum Entropy ◽  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Simple Formula ◽  
Matrix Theory ◽  
Inviscid Flow ◽  
Two Dimensional ◽  
Cylindrically Symmetric ◽  
Vortex Field

We derive a formula for the entropy of two-dimensional incompressible inviscid flow, by determining the volume of the space of vorticity distributions with fixed values for the moments Qk = ∫ ω(x)kd2x. This space is approximated by a sequence of spaces of finite volume, by using a regularization of the system that is geometrically natural and connected with the theory of random matrices. By taking the limit we get a simple formula for the entropy of a vortex field. We predict vorticity distributions of maximum entropy with given mean vorticity and enstrophy; we also predict the cylindrically symmetric vortex field with maximum entropy. This could be an approximate description of a hurricane.

scholarly journals Page curve for entanglement negativity through geometric evaporation

2022 ◽  
Vol 12 (1) ◽  
Author(s):  
Jaydeep Kumar Basak ◽  
Debarshi Basu ◽  
Vinay Malvimat ◽  
Himanshu Parihar ◽  
Gautam Sengupta
Keyword(s):  
Black Hole ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Mixed State ◽  
Dimensional Reduction ◽  
Matrix Theory ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Btz Black Hole ◽  
Diagrammatic Technique

We compute the entanglement negativity for various pure and mixed state configurations in a bath coupled to an evaporating two dimensional non-extremal Jackiw-Teitelboim (JT) black hole obtained through the partial dimensional reduction of a three dimensional BTZ black hole. Our results exactly reproduce the analogues of the Page curve for the entanglement negativity which were recently determined through diagrammatic technique developed in the context of random matrix theory.

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.

Introduction and guide to the handbook

2018 ◽  
Author(s):  
Gernot Akemann ◽  
Jinho Baik ◽  
Philippe Di Francesco
Keyword(s):  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
The Other ◽  
Random Operators ◽  
New Developments ◽  
Gaussian Unitary Ensemble ◽  
Mathematical Properties ◽  
Unitary Ensemble

This article discusses random matrix theory (RMT) in a nutshell — what it is about, what its main features are, and why it is so successful in applications. It first considers the simplest and maybe most frequently used standard example, the Gaussian Unitary Ensemble (GUE) of random matrices, before looking at several types of applications of RMT, focusing on random operators, counting devices, and RMT without matrices. It then provides a guide to the handbook, explaining how the other forty-two articles on mathematical properties and applications of random matrices are related and built one upon the other. It also lists some topics that are not covered in detail in the book and reviews recent new developments since the first edition of this handbook before concluding with a brief survey of the existing introductory literature.

scholarly journals Octonions in random matrix theory

2017 ◽  
Vol 473 (2200) ◽  
pp. 20160800 ◽  
Author(s):  
Peter J. Forrester
Keyword(s):  
Random Matrices ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Quantum Physics ◽  
Matrix Theory ◽  
Analytic Theory ◽  
Division Algebras ◽  
Number Systems ◽  
The Matrix ◽  
Real Complex

The octonions are one of the four normed division algebras, together with the real, complex and quaternion number systems. The latter three hold a primary place in random matrix theory, where in applications to quantum physics they are determined as the entries of ensembles of Hermitian random matrices by symmetry considerations. Only for N =2 is there an existing analytic theory of Hermitian random matrices with octonion entries. We use a Jordan algebra viewpoint to provide an analytic theory for N =3. We then proceed to consider the matrix structure X † X , when X has random octonion entries. Analytic results are obtained from N =2, but are observed to break down in the 3×3 case.

SSA, Random Matrix Theory, and Noise-Reduced Correlations

2016 ◽  
Author(s):  
Jan W Dash ◽  
Xipei Yang ◽  
Mario Bondioli ◽  
Harvey J. Stein
Keyword(s):  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory
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