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We classify SU(3) gauge field configurations in different topological sectors by the smearing technique. In each sector we compute the distribution of low lying eigenvalues of the staggered Dirac operator. In all sectors we find perfect…

High Energy Physics - Lattice · Physics 2015-06-25 P. H. Damgaard , U. M. Heller , R. Niclasen , K. Rummukainen

Complete spectra of the staggered Dirac operator $\Dirac$ are determined in quenched four-dimensional $SU(2)$ gauge fields, and also in the presence of dynamical fermions. Periodic as well as antiperiodic boundary conditions are used. An…

High Energy Physics - Lattice · Physics 2009-10-22 Thomas Kalkreuter

We analyze Dirac spectra of two-dimensional QCD like theories both in the continuum and on the lattice and classify them according to random matrix theories sharing the same global symmetries. The classification is different from QCD in…

High Energy Physics - Lattice · Physics 2014-10-22 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

We study the spectrum of the staggered Dirac operator in SU(2) gauge fields close to the free limit, for both the fundamental and the adjoint representation. Numerically we find a characteristic cluster structure with spacings of adjacent…

High Energy Physics - Lattice · Physics 2008-11-26 Falk Bruckmann , Stefan Keppeler , Marco Panero , Tilo Wettig

In this paper we study a random matrix model with the chiral and flavor structure of the QCD Dirac operator and a temperature dependence given by the lowest Matsubara frequency. Using the supersymmetric method for random matrix theory, we…

High Energy Physics - Phenomenology · Physics 2009-10-28 A. D. Jackson , M. K. Şener , J. J. M. Verbaarschot

According to the Banks-Casher formula the chiral order parameter is directly related to the spectrum of the Dirac operator. In this lecture, we will argue that some properties of the Dirac spectrum are universal and can be obtained from a…

High Energy Physics - Phenomenology · Physics 2007-05-23 J. J. M. Verbaarschot

Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…

High Energy Physics - Phenomenology · Physics 2009-10-31 J. J. M. Verbaarschot , T. Wettig

In this lecture we discuss correlations of the QCD Dirac eigenvalues. We find that below a scale of $E_c\sim \Lambda/L^2$ they are given by chiral Random Matrix Theory. This follows from analytical arguments based on partially quenched…

High Energy Physics - Theory · Physics 2007-05-23 J. J. M. Verbaarschot

We study the spectrum of the QCD Dirac operator near zero virtuality for $N_c =2$. According to a universality argument, it can be described by a random matrix theory with the chiral structure of QCD, but with $real$ matrix elements. Using…

High Energy Physics - Theory · Physics 2009-10-28 Jacobus Verbaarschot

The application of Random Matrix Theory to the Dirac operator of QCD yields predictions for the probability distributions of the lowest eigenvalues. We measured Dirac operator spectra using massless overlap fermions in quenched QCD at…

High Energy Physics - Lattice · Physics 2009-11-10 S. Shcheredin , W. Bietenholz , T. Chiarappa , K. Jansen , K. -I. Nagai

The correlations of the QCD Dirac eigenvalues are studied with use of an extended chiral random matrix model. The inclusion of spatial dependence which the original model lacks enables us to investigate the effects of diffusion modes. We…

High Energy Physics - Theory · Physics 2009-10-31 K. Takahashi , S. Iida

We compute the microscopic spectrum of the QCD Dirac operator in the presence of dynamical fermions in the framework of random-matrix theory for the chiral Gaussian unitary ensemble. We obtain results for the microscopic spectral…

High Energy Physics - Theory · Physics 2009-10-30 T. Wilke , T. Guhr , T. Wettig

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

We propose a random matrix model that interpolates between the chiral random matrix ensembles and the chiral Poisson ensemble. By mapping this model on a non-interacting Fermi-gas we show that for energy differences less than a critical…

High Energy Physics - Theory · Physics 2016-09-06 A. M. Garcia-Garcia , J. J. M. Verbaarschot

In these two lectures given at the 1997 Zakopane workshop on "New Developments in Quantum Field Theory" we review recent results on universal fluctuations in QCD Dirac spectra. We start the first lecture with a review of some general…

High Energy Physics - Theory · Physics 2007-05-23 J. J. M. Verbaarschot

The microscopic spectral eigenvalue correlations of QCD Dirac operators in the presence of dynamical fermions are calculated within the framework of Random Matrix Theory (RMT). Our approach treats the low--energy correlation functions of…

High Energy Physics - Lattice · Physics 2008-11-26 G. Akemann , E. Kanzieper

We compute individual distributions of low-lying eigenvalues of a chiral random matrix ensemble interpolating symplectic and unitary symmetry classes by the Nystr\"om-type method of evaluating the Fredholm Pfaffian and resolvents of the…

High Energy Physics - Lattice · Physics 2018-02-20 Takuya Yamamoto , Shinsuke M. Nishigaki

We compare analytic predictions of non-Hermitian chiral random matrix theory with the complex Dirac operator eigenvalue spectrum of two-colour lattice gauge theory with dynamical fermions at nonzero chemical potential. The Dirac eigenvalues…

High Energy Physics - Lattice · Physics 2009-11-11 G. Akemann , E. Bittner

As was shown by Leutwyler and Smilga, the fact that chiral symmetry is broken and the existence of a effective finite volume partition function leads to an infinite number of sum rules for the eigenvalues of the Dirac operator in QCD. In…

High Energy Physics - Theory · Physics 2009-09-25 Jacobus Verbaarschot

We analyze the eigenvalue statistics of the staggered Dirac operator above $T_{c}$ in QCD with 2+1 flavors of dynamical quarks. We use physical quark masses in our simulations. We compare the eigenvalue statistics from several parts of the…

High Energy Physics - Lattice · Physics 2011-11-16 Tamás G. Kovács , Ferenc Pittler