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Related papers: Individual Eigenvalue Distributions for the Wilson…

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We compute the low lying eigenvalues of the Hermitian Dirac operator in lattice QCD with $N_{\rm f} = 2+1+1$ twisted mass fermions. We discuss whether these eigenvalues are in the $\epsilon$-regime or the $p$-regime of Wilson chiral…

High Energy Physics - Lattice · Physics 2018-11-29 Krzysztof Cichy , Savvas Zafeiropoulos

The spectral flow of the low-lying eigenvalues of the improved and unimproved Wilson-Dirac operator is studied on instanton-like configurations and on thermalized quenched configurations at various $\beta$-values and lattice sizes. We also…

High Energy Physics - Lattice · Physics 2007-05-23 Hubert Simma , Douglas Smith

Starting from the chiral Lagrangian for Wilson fermions at nonzero lattice spacing we have obtained compact expressions for all spectral correlation functions of the Hermitian Wilson Dirac operator in the $\epsilon$-domain of QCD with…

High Energy Physics - Lattice · Physics 2011-12-05 K. Splittorff , J. J. M. Verbaarschot

We compute individual distributions of low-lying eigenvalues of massive chiral random matrix ensembles by the Nystr\"om-type quadrature method for evaluating the Fredholm determinant and Pfaffian that represent the analytic continuation of…

High Energy Physics - Lattice · Physics 2019-09-04 Hiroyuki Fuji , Issaku Kanamori , Shinsuke M. Nishigaki

We study the lattice artefacts of the Wilson Dirac operator for QCD with two colors and fermions in the fundamental representation from the viewpoint of chiral perturbation theory. These effects are studied with the help of the following…

High Energy Physics - Lattice · Physics 2015-08-26 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

Bandlimiting and timelimiting operators play a fundamental role in analyzing bandlimited signals that are approximately timelimited (or vice versa). In this paper, we consider a time-frequency (in the discrete Fourier transform (DFT)…

Information Theory · Computer Science 2018-02-14 Zhihui Zhu , Santhosh Karnik , Mark A. Davenport , Justin Romberg , Michael B. Wakin

Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.

High Energy Physics - Theory · Physics 2009-10-31 P. H. Damgaard , S. M. Nishigaki

We compute the lattice spacing corrections to the spectral density of the Hermitean Wilson Dirac operator using Wilson Chiral Perturbation Theory at NLO. We consider a regime where the quark mass $m$ and the lattice spacing $a$ obey the…

High Energy Physics - Lattice · Physics 2015-05-27 S. Necco , A. Shindler

We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential \mu for a…

High Energy Physics - Phenomenology · Physics 2009-05-29 Kenji Fukushima

Random Matrix Theory has been successfully applied to lattice Quantum Chromodynamics. In particular, a great deal of progress has been made on the understanding, numerically as well as analytically, of the spectral properties of the Wilson…

High Energy Physics - Lattice · Physics 2013-11-13 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

In this paper we study the interior transmission problem and transmission eigenvalues for multiplicative perturbations of linear partial differential operator of order $\ge 2$ with constant real coefficients. Under suitable growth…

Mathematical Physics · Physics 2015-03-17 Michael Hitrik , Katsiaryna Krupchyk , Petri Ola , Lassi Päivärinta

We report on the behavior of the eigenvalue distribution of the Dirac operator in (2+1)-flavor QCD at finite temperature, using the HISQ action. We calculate the eigenvalue density at several values of the temperature close to the…

High Energy Physics - Lattice · Physics 2012-02-21 H. Ohno , U. M. Heller , F. Karsch , S. Mukherjee

We study the fluctuation behavior of individual eigenvalues of kernel matrices arising from dense graphon-based random graphs. Under minimal integrability and boundedness assumptions on the graphon, we establish distributional limits for…

Probability · Mathematics 2026-03-03 Behzad Aalipur

We summarize the analytical solution of the Chiral Perturbation Theory for the Hermitian Wilson Dirac operator of $N_c=2$ QCD with quarks in the fundamental representation. Results have been obtained for the quenched microscopic spectral…

High Energy Physics - Lattice · Physics 2015-05-20 Mario Kieburg , Jacobus Verbaarschot , Savvas Zafeiropoulos

An exploratory study of the low-lying eigenvalues of the Wilson-Dirac operator and their corresonding eigenvectors is presented. Results for the eigenvalues from quenched and unquenched simulations are discussed. The eigenvectors are…

High Energy Physics - Lattice · Physics 2009-10-28 K. Jansen , C. Liu , H. Simma , D. Smith

In this work we continue the study of the Weyl asymptotics of the distribution of eigenvalues of non-self-adjoint (pseudo)differential operators with small random perturbations, by treating the case of multiplicative perturbations in…

Spectral Theory · Mathematics 2009-12-02 Johannes Sjoestrand

In this paper, we consider the problem of deriving new eigenvalue distributions of real-valued Wishart matrices that arises in many scientific and engineering applications. The distributions are derived using the tools from the theory of…

Information Theory · Computer Science 2015-07-29 Oliver James , Heung-No Lee

We consider quite general $h$-pseudodifferential operators on $R^n$ with small random perturbations and show that in the limit of small $h$ the eigenvalues are distributed according to a Weyl law with a probabality that tends to 1. The…

Spectral Theory · Mathematics 2007-05-23 Mildred Hager , Johannes Sjoestrand

The QCD partition function for the Wilson Dirac operator, $D_W$, at nonzero lattice spacing $a$ can be expressed in terms of a chiral Lagrangian as a systematic expansion in the quark mass, the momentum and $a^2$. Starting from this chiral…

High Energy Physics - Lattice · Physics 2011-07-15 G. Akemann , P. H. Damgaard , K. Splittorff , J. J. M. Verbaarschot

We estimate the distribution of the eigenvalues of a family of time-frequency localization operators whose eigenfunctions are the well-known Prolate Spheroidal Wave Functions from mathematical physics. These operators are fundamental to the…

Classical Analysis and ODEs · Mathematics 2015-02-17 Arie Israel