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Related papers: Eigenvalue Density of the non-Hermitian Wilson Dir…

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The goal of this article is to study how much the eigenvalues of large Hermitian random matrices deviate from certain deterministic locations -- or in other words, to investigate optimal rigidity estimates for the eigenvalues. We do this in…

Probability · Mathematics 2019-06-05 Tom Claeys , Benjamin Fahs , Gaultier Lambert , Christian Webb

We consider properties of zero and near-zero modes for overlap fermion operator in SU(2) lattice gluodynamics. The density of the states is of the order of Lambda(QCD) while the localization volume of the modes tends to zero in physical…

High Energy Physics - Lattice · Physics 2007-05-23 M. I. Polikarpov , F. V. Gubarev , S. M. Morozov , V. I. Zakharov

We reconsider the recently proposed connection between density of states in the so-called ``non-hermitian quantum mechanics'' and the localization length for a particle moving in random potential. We argue that it is indeed possible to find…

Disordered Systems and Neural Networks · Physics 2009-10-31 Christopher Mudry , P. W. Brouwer , B. I. Halperin , V. Gurarie , A. Zee

We investigate the distribution of low-lying eigenmodes of hermitian Wilson-Dirac operator, $H_W$, with the gauge action whose form is designed to avoid topology change, as well as with the standard plaquette action. On the quenched…

High Energy Physics - Lattice · Physics 2009-04-25 H. Fukaya , S. Hashimoto , T. Hirohashi , H. Matsufuru , K. Ogawa , T. Onogi

The average density of states (DoS) of the one-dimensional Dirac Hamiltonian with a random mass on a finite interval [0,L] is derived. Our method relies on the eigenvalues distributions (extreme value statistics problem) which are…

Disordered Systems and Neural Networks · Physics 2009-12-11 Christophe Texier , Christian Hagendorf

We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…

High Energy Physics - Lattice · Physics 2016-05-27 Zoltan Fodor , Kieran Holland , Julius Kuti , Santanu Mondal , Daniel Nogradi , Chik Him Wong

We introduce a random two-matrix model interpolating between a chiral Hermitian (2n+nu)x(2n+nu) matrix and a second Hermitian matrix without symmetries. These are taken from the chiral Gaussian Unitary Ensemble (chGUE) and Gaussian Unitary…

Mathematical Physics · Physics 2011-11-03 Gernot Akemann , Taro Nagao

We study numerically the localization properties of eigenstates in a one-dimensional random lattice described by a non-Hermitian disordered Hamiltonian, where both the disorder and the non-Hermiticity are inserted simultaneously in the…

Disordered Systems and Neural Networks · Physics 2020-01-08 Ba Phi Nguyen , Duy Khuong Phung , Kihong Kim

The dependence of the overlap Dirac operator on the Wilson-mass regulator parameter is studied through calculations of the overlap topological charge densities at a variety of Wilson-mass values. In this formulation, the Wilson-mass is used…

High Energy Physics - Lattice · Physics 2011-06-27 Peter J. Moran , Derek B. Leinweber , Jianbo Zhang

We derive the exact form of the eigenvalue spectra of correlation matrices derived from a set of time-shifted, finite Brownian random walks (time-series). These matrices can be seen as random, real, asymmetric matrices with a special…

Physics and Society · Physics 2008-12-02 Christoly Biely , Stefan Thurner

We study Anderson localization of non-interacting random hopping fermions on bipartite lattices in two dimensions, focusing our attention to strong disorder features of the model. We concentrate ourselves on specific models with a linear…

Disordered Systems and Neural Networks · Physics 2009-11-10 H. Yamada , T. Fukui

The eigenvalue density for members of the Gaussian orthogonal and unitary ensembles follows the Wigner semi-circle law. If the Gaussian entries are all shifted by a constant amount c/Sqrt(2N), where N is the size of the matrix, in the large…

Mathematical Physics · Physics 2009-04-21 Kevin E. Bassler , Peter J. Forrester , Norman E. Frankel

We study statistical properties of the eigenvectors of non-Hermitian random matrices, concentrating on Ginibre's complex Gaussian ensemble, in which the real and imaginary parts of each element of an N x N matrix, J, are independent random…

Disordered Systems and Neural Networks · Physics 2009-10-31 J. T. Chalker , B. Mehlig

We analyze how individual eigenvalues of the QCD Dirac operator at nonzero quark chemical potential are distributed in the complex plane. Exact and approximate analytical results for both quenched and unquenched distributions are derived…

High Energy Physics - Lattice · Physics 2008-11-26 G. Akemann , J. Bloch , L. Shifrin , T. Wettig

We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition…

High Energy Physics - Lattice · Physics 2008-11-26 Christof Gattringer , Meinulf Goeckeler , P. E. L. Rakow , Stefan Schaefer , Andreas Schaefer

The aim of this work is to explore the discrete spectrum generated by complex perturbations in $L^{2}(\mathbb{R}^3,\mathbb{C}^4)$ of the $3d$ Dirac operator $\alpha \cdot (-i\nabla - \textbf{A}) + m \beta$ with variable magnetic field.…

Spectral Theory · Mathematics 2016-12-08 Diomba Sambou

Within the framework of non-Hermitian photonics, we investigate the spectral and dynamical properties of one- and two-dimensional non-Hermitian off-diagonal disordered optical lattices, where randomness is applied to the couplings rather…

Disordered Systems and Neural Networks · Physics 2026-05-28 E. T. Kokkinakis , I. Komis , K. G. Makris , E. N. Economou

The density matrix, \rho, of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are three orders…

Mesoscale and Nanoscale Physics · Physics 2013-05-29 Carlos Andres Vera , Alejandro Cabo , Augusto Gonzalez

We study several classes of non-Hermitian Hamiltonian systems, which can be expressed in terms of bilinear combinations of Euclidean Lie algebraic generators. The classes are distinguished by different versions of antilinear (PT)-symmetries…

Quantum Physics · Physics 2014-04-29 Sanjib Dey , Andreas Fring , Thilagarajah Mathanaranjan

We determine the density of eigenvalues of the scattering matrix of the Schrodinger operator with a short range potential in the high energy asymptotic regime. We give an explicit formula for this density in terms of the X-ray transform of…

Spectral Theory · Mathematics 2015-05-30 Daniel Bulger , Alexander Pushnitski