scholarly journals Onset of universality in the dynamical mixing of a pure state

2021 ◽  
Author(s):  
M. Carrera-Núñez ◽  
A. M. Martínez-Argüello ◽  
J. M. Torres ◽  
E. J. Torres-Herrera
Keyword(s):  
Pure State ◽  
Matrix Theory ◽  
Chaotic Regime ◽  
Many Body ◽  
Analytical Treatment ◽  
Gaussian Unitary Ensemble ◽  
Time Dynamics ◽  
Spectral Statistics ◽  
Gaussian Orthogonal Ensemble ◽  
Unitary Ensemble

Abstract We study the time dynamics of random density matrices generated by evolving the same pure state using a Gaussian orthogonal ensemble (GOE) of Hamiltonians. We show that the spectral statistics of the resulting mixed state is well described by random matrix theory (RMT) and undergoes a crossover from the Gaussian orthogonal ensemble to the Gaussian unitary ensemble (GUE) for short and large times, respectively. Using a semi-analytical treatment relying on a power series of the density matrix as a function of time, we find that the crossover occurs in a characteristic time that scales as the inverse of the dimension. The RMT results are contrasted with a paradigmatic model of many-body localization in the chaotic regime, where the GUE statistics is reached at large times, while for short times the statistics strongly depends on the peculiarity of the considered subspace.

Generalization of Brody distribution for statistical investigation

2014 ◽  
Vol 03 (04) ◽  
pp. 1450017 ◽  
Author(s):  
H. Sabri ◽  
Sh. S. Hashemi ◽  
B. R. Maleki ◽  
M. A. Jafarizadeh
Keyword(s):  
Nearest Neighbor ◽  
Matrix Theory ◽  
Likelihood Estimation ◽  
Statistical Investigation ◽  
Distribution Functions ◽  
Estimation Methods ◽  
General Distribution ◽  
Gaussian Unitary Ensemble ◽  
Gaussian Orthogonal Ensemble ◽  
Unitary Ensemble

In this paper, Brody distribution is generalized to explore the Poisson, Gaussian Orthogonal Ensemble and Gaussian Unitary Ensemble limits of Random Matrix Theory in the nearest neighbor spacing statistic framework. Parameters of new distribution are extracted via Maximum Likelihood Estimation technique for different sequences. This general distribution suggests more exact results in comparison with the results of other estimation methods and distribution functions.

scholarly journals Replica approach in random matrix theory

2018 ◽  
Author(s):  
Thomas Guhr
Keyword(s):  
Partition Function ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Field Theories ◽  
Partition Functions ◽  
Gaussian Unitary Ensemble ◽  
Integrable Theory ◽  
Unitary Ensemble ◽  
Replica Approach

This article examines the replica method in random matrix theory (RMT), with particular emphasis on recently discovered integrability of zero-dimensional replica field theories. It first provides an overview of both fermionic and bosonic versions of the replica limit, along with its trickery, before discussing early heuristic treatments of zero-dimensional replica field theories, with the goal of advocating an exact approach to replicas. The latter is presented in two elaborations: by viewing the β = 2 replica partition function as the Toda lattice and by embedding the replica partition function into a more general theory of τ functions. The density of eigenvalues in the Gaussian Unitary Ensemble (GUE) and the saddle point approach to replica field theories are also considered. The article concludes by describing an integrable theory of replicas that offers an alternative way of treating replica partition functions.

scholarly journals The universe from a single particle

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Michael Freedman ◽  
Modjtaba Shokrian Zini
Keyword(s):  
Quantum Mechanics ◽  
Single Particle ◽  
Quantum Mechanical ◽  
Local Minima ◽  
Quantum Mechanical System ◽  
Many Body ◽  
Gaussian Unitary Ensemble ◽  
Interacting Systems ◽  
The Universe ◽  
Unitary Ensemble

Abstract We explore the emergence of many-body physics from quantum mechanics via spontaneous symmetry breaking. To this end, we study potentials which are functionals on the space of Hamiltonians enjoying an unstable critical point corresponding to a random quantum mechanical system (the Gaussian unitary ensemble), but also less symmetrical local minima corresponding to interacting systems at the level of operators.

scholarly journals Distribution of the Dirac modes in QCD

2018 ◽  
Vol 175 ◽  
pp. 04005
Author(s):  
M. Catillo ◽  
L. Ya. Glozman
Keyword(s):  
Dirac Operator ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
General Property ◽  
Matrix Theory ◽  
Spontaneous Breaking ◽  
Gaussian Unitary Ensemble ◽  
Zero Modes ◽  
Dynamical Simulations ◽  
Unitary Ensemble

It was established that distribution of the near-zero modes of the Dirac operator is consistent with the Chiral Random Matrix Theory (CRMT) and can be considered as a consequence of spontaneous breaking of chiral symmetry (SBCS) in QCD. The higherlying modes of the Dirac operator carry information about confinement physics and are not affected by SBCS. We study distributions of the near-zero and higher-lying modes of the overlap Dirac operator within NF = 2 dynamical simulations. We find that distributions of both near-zero and higher-lying modes are the same and follow the Gaussian Unitary Ensemble of Random Matrix Theory. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is related to some more general property of QCD in confinement regime.

scholarly journals Distribution law of the Dirac eigenmodes in QCD

2018 ◽  
Vol 33 (10) ◽  
pp. 1850054
Author(s):  
Marco Catillo ◽  
Leonid Ya. Glozman
Keyword(s):  
Dirac Operator ◽  
Random Matrix Theory ◽  
Random Matrix ◽  
Matrix Theory ◽  
Spontaneous Breaking ◽  
Distribution Law ◽  
Gaussian Unitary Ensemble ◽  
Zero Modes ◽  
Dynamical Simulations ◽  
Unitary Ensemble

The near-zero modes of the Dirac operator are connected to spontaneous breaking of chiral symmetry in QCD (SBCS) via the Banks–Casher relation. At the same time, the distribution of the near-zero modes is well described by the Random Matrix Theory (RMT) with the Gaussian Unitary Ensemble (GUE). Then, it has become a standard lore that a randomness, as observed through distributions of the near-zero modes of the Dirac operator, is a consequence of SBCS. The higher-lying modes of the Dirac operator are not affected by SBCS and are sensitive to confinement physics and related [Formula: see text] and [Formula: see text] symmetries. We study the distribution of the near-zero and higher-lying eigenmodes of the overlap Dirac operator within [Formula: see text] dynamical simulations. We find that both the distributions of the near-zero and higher-lying modes are perfectly described by GUE of RMT. This means that randomness, while consistent with SBCS, is not a consequence of SBCS and is linked to the confining chromo-electric field.

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.

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