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Related papers: Eigenvalue Distributions of the QCD Dirac Operator

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We use a chiral random matrix model to investigate the effects of massive quarks on the distribution of eigenvalues of QCD inspired Dirac operators. Kalkreuter's lattice analysis of the spectrum of the massive (hermitean) Dirac operator for…

High Energy Physics - Phenomenology · Physics 2009-10-28 Jerzy Jurkiewicz , Maciej A. Nowak , Ismail Zahed

The zero momentum sectors in effective theories of QCD coupled to pseudoreal (two colors) and real (adjoint) quarks have alternative descriptions in terms of chiral orthogonal and symplectic ensembles of random matrices. Using this…

High Energy Physics - Theory · Physics 2009-10-31 T. Nagao , S. M. Nishigaki

The zero momentum sectors in effective theories of three dimensional QCD coupled to pseudoreal (two colors) and real (adjoint) quarks in a classically parity-invariant manner have alternative descriptions in terms of orthogonal and…

High Energy Physics - Theory · Physics 2016-09-06 T. Nagao , S. M. Nishigaki

We provide first evidence that Matrix Models describe the low lying complex Dirac eigenvalues in a theory with dynamical fermions at non-zero density. Lattice data for gauge group SU(2) with staggered fermions are compared to detailed…

High Energy Physics - Lattice · Physics 2007-05-23 Gernot Akemann , Elmar Bittner

Based on the chiral symmetry breaking pattern and the corresponding low-energy effective lagrangian, we determine the fermion mass dependence of the partition function and derive sum rules for eigenvalues of the QCD Dirac operator in finite…

High Energy Physics - Theory · Physics 2008-11-26 A. Smilga , J. Verbaarschot

We present simulation results for lattice QCD with chiral fermions in small volumes, where the epsilon-expansion of chiral perturbation theory applies. Our data for the low lying Dirac eigenvalues, as well as mesonic correlation functions,…

High Energy Physics - Lattice · Physics 2009-11-11 W. Bietenholz , T. Chiarappa , K. Jansen , K. -I. Nagai , S. Shcheredin

In Quantum Chromodynamics (QCD) the eigenmodes of the Dirac operator with small absolute eigenvalues have a close relationship to the dynamical breaking of the chiral symmetry. In a simulation with two dynamical quarks, we study the…

High Energy Physics - Lattice · Physics 2015-03-19 C. B. Lang , Mario Schröck

We investigate the spectrum of the staggered Dirac operator in 4d quenched U(1) lattice gauge theory and its relationship to random matrix theory. In the confined as well as in the Coulomb phase the nearest-neighbor spacing distribution of…

High Energy Physics - Lattice · Physics 2015-06-25 Bernd A. Berg , Harald Markum , Rainer Pullirsch , Tilo Wettig

I propose a simple model of the distribution of the small eigenvalues of the QCD Dirac operator well above the finite temperature phase transition where chiral symmetry is restored and the spectral density at zero vanishes. Assuming the…

High Energy Physics - Lattice · Physics 2010-11-11 Tamas G. Kovacs

Recently, a non-Hermitian chiral random matrix model was proposed to describe the eigenvalues of the QCD Dirac operator at nonzero chemical potential. This matrix model can be constructed from QCD by mapping it to an equivalent matrix model…

High Energy Physics - Lattice · Physics 2009-11-10 G. Akemann , T. Wettig

We have calculated complete spectra of the staggered Dirac operator on the lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice sizes. The microscopic spectral density, the distribution of the smallest eigenvalue, and…

High Energy Physics - Lattice · Physics 2008-11-26 M. Göckeler , H. Hehl , P. E. L. Rakow , A. Schäfer , T. Wettig

We calculate the chiral condensate of QCD with 2, 2+1 and 3 flavors of sea quarks. Lattice QCD simulations are performed employing dynamical overlap fermions with up and down quark masses covering a range between 3 and 100 MeV. On L ~…

High Energy Physics - Lattice · Physics 2015-03-17 H. Fukaya , S. Aoki , T. W. Chiu , S. Hashimoto , T. Kaneko , J. Noaki , T. Onogi , N. Yamada

Using relations from random matrix theory, we derive exact expressions for all $n$-point spectral correlation functions of Dirac operator eigenvalues in terms of finite-volume partition functions. This is done for both chiral symplectic and…

High Energy Physics - Theory · Physics 2009-10-31 G. Akemann , P. H. Damgaard

We show that the lowest part of the eigenvalue density of the staggered fermion operator in lattice QCD_3 at small lattice coupling constant beta has exactly the same shape as in QCD_4. This observation is quite surprising, since universal…

High Energy Physics - Lattice · Physics 2011-02-28 P. Bialas , Z. Burda , B. Petersson

Eigenvalues and eigenfunctions of the QCD Dirac operator are studied for gauge field configurations given by a liquid of instantons. We find that for energy differences $\delta E$ below an energy scale $E_c$ the eigenvalue correlations are…

High Energy Physics - Phenomenology · Physics 2009-10-31 J. C. Osborn , J. J. M. Verbaarschot

The low-lying spectrum of the Dirac operator is predicted to be universal, within three classes, depending on symmetry properties specified according to random matrix theory. The three universal classes are the orthogonal, unitary and…

High Energy Physics - Lattice · Physics 2009-10-31 Robert G. Edwards , Urs M. Heller , Rajamani Narayanan

We compute the condensate in QCD with two flavors of dynamical fermions using numerical simulation. The simulations use overlap fermions, and the condensate is extracted by fitting the distribution of low lying eigenvalues of the Dirac…

High Energy Physics - Lattice · Physics 2014-11-17 Thomas DeGrand , Zhaofeng Liu , Stefan Schaefer

We discuss a new Random Matrix Model for QCD with a chemical potential that is based on the symmetries of the Dirac operator and can be solved exactly for all eigenvalue correlations for any number of flavors. In the microscopic limit of…

High Energy Physics - Lattice · Physics 2009-11-10 James C. Osborn

We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…

High Energy Physics - Lattice · Physics 2009-10-31 F. Farchioni , I. Hip , C. B. Lang , M. Wohlgenannt

We provide quantitative estimates on the location of eigenvalues of one-dimensional discrete Dirac operators with complex $\ell^p$-potentials for $1\leq p\leq\infty$. As a corollary, subsets of the essential spectrum free of embedded…

Spectral Theory · Mathematics 2020-08-25 Biagio Cassano , Orif O. Ibrogimov , David Krejcirik , Frantisek Stampach