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Related papers: The k-th Smallest Dirac Operator Eigenvalue and th…

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We generated configurations with the parametrized fixed-point Dirac operator D_{FP} on a (1.6 fm)^4 box at a lattice spacing a=0.13 fm. We compare the distributions of the three lowest k=1,2,3 eigenvalues in the nu= 0,1,2 topological…

High Energy Physics - Lattice · Physics 2014-11-18 P. Hasenfratz , D. Hierl , V. Maillart , F. Niedermayer , A. Schäfer , C. Weiermann , M. Weingart

We study the eigenvalues of Dirac operators in QCD with two mass degenerate dynamical fermions. The gauge configurations have been obtained with HMC and the so-called Chirally Improved fermionic action. We compare eigenvalues obtained for…

High Energy Physics - Lattice · Physics 2009-04-14 Martina Joergler , C. B. Lang

We consider the effect of discretization errors on the microscopic spectrum of the Wilson Dirac operator using both chiral Perturbation Theory and chiral Random Matrix Theory. A graded chiral Lagrangian is used to evaluate the microscopic…

High Energy Physics - Lattice · Physics 2015-03-17 G. Akemann , P. H. Damgaard , K. Splittorff , J. J. M. Verbaarschot

The low-lying eigenvalue spectrum of the QCD Dirac operator in the epsilon-regime is expected to match with that of chiral Random Matrix Theory (ChRMT). We study this correspondence for the case including sea quarks by performing two-flavor…

High Energy Physics - Lattice · Physics 2012-08-27 JLQCD , TWQCD collaboration , : , H. Fukaya , S. Aoki , T. W. Chiu , S. Hashimoto , T. Kaneko , H. Matsufuru , J. Noaki , K. Ogawa , T. Onogi , N. Yamada

We derive spectral sum rules for a system with two quarks coupled to an imaginary isospin chemical potential in the \epsilon regime. The sum rules show an explicit dependence on the pion decay constant which should make it possible to…

High Energy Physics - Lattice · Physics 2009-11-11 Magdalena Luz

As increased statistics and new ensembles with light pions have become available within the CLS effort, we complete previous work by inspecting the chiral behaviour of the pion decay constant. We discuss the validity of Chiral Perturbation…

High Energy Physics - Lattice · Physics 2013-11-26 Stefano Lottini

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

We investigate the eigenvalues and eigenvectors of the staggered Dirac operator in the vicinity of the chiral phase transition of quenched SU(3) lattice gauge theory. We consider both the global features of the spectrum and the local…

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

We present a calculation of the low energy constants describing the real and imaginary parts of the $K \to \pi \pi$ decay amplitudes $A_0$ and $A_2$. Leading and next leading order chiral perturbation theory is used and its applicability…

High Energy Physics - Lattice · Physics 2010-01-21 Shu Li , Norman H. Christ

We analyze complete spectra of the lattice Dirac operator in SU(2) gauge theory and demonstrate that the distribution of low-lying eigenvalues is described by random matrix theory. We present possible practical applications of this…

High Energy Physics - Lattice · Physics 2009-10-30 M. E. Berbenni-Bitsch , A. D. Jackson , S. Meyer , A. Schäfer , J. J. M. Verbaarschot , T. Wettig

We continue our investigation of the QCD dynamics in terms of the Curci-Ferrari effective Lagrangian, a deformation of the Faddeev-Popov one in the Landau gauge with a tree-level gluon mass term. In a previous work we have studied the…

High Energy Physics - Phenomenology · Physics 2023-03-29 Marcela Peláez , Urko Reinosa , Julien Serreau , Nicolás Wschebor

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

Consider the Coulomb potential $-\mu\ast|x|^{-1}$ generated by a non-negative finite measure $\mu$. It is well known that the lowest eigenvalue of the corresponding Schr\"odinger operator $-\Delta/2-\mu\ast|x|^{-1}$ is minimized, at fixed…

Spectral Theory · Mathematics 2023-10-31 Maria J. Esteban , Mathieu Lewin , Éric Séré

The Dirac operator in finite temperature QCD is equivalent to the Hamiltonian of an unconventional Anderson model, with on-site noise provided by the fluctuations of the Polyakov lines. The main features of its spectrum and eigenvectors,…

High Energy Physics - Lattice · Physics 2017-04-27 Matteo Giordano , Tamas G. Kovacs , Ferenc Pittler

When chiral symmetry is spontaneously broken, the low-energy part of the Dirac operator spectrum can be computed analytically in the chiral limit. The tool is effective field theory or, equivalently in this case, Random Matrix Theory.

High Energy Physics - Phenomenology · Physics 2007-05-23 P. H. Damgaard

We study the spectrum of the hermitian Wilson Dirac operator in the epsilon-regime of QCD in the quenched approximation and compare it to predictions from Wilson Random Matrix Theory. Using the distributions of single eigenvalues in the…

High Energy Physics - Lattice · Physics 2011-12-22 Albert Deuzeman , Urs Wenger , Jaïr Wuilloud

We investigate the distribution of the spacings of adjacent eigenvalues of the lattice Dirac operator. At zero chemical potential $\mu$, the nearest-neighbor spacing distribution $P(s)$ follows the Wigner surmise of random matrix theory…

High Energy Physics - Lattice · Physics 2009-10-31 H. Markum , R. Pullirsch , K. Rabitsch , T. Wettig

By computing the Dirac operator spectrum by means of Numerical Stochastic Perturbation Theory, we aim at throwing some light on the widely accepted picture for the mechanism which is behind the Bank-Casher relation. The latter relates the…

High Energy Physics - Lattice · Physics 2010-02-03 M. Brambilla , F. Di Renzo

This thesis is dedicated to explore the feasibility of numerical calculations in the $\epsilon$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and…

High Energy Physics - Lattice · Physics 2007-05-23 S. Shcheredin

We discuss insights that may be drawn from our recent 2 flavour O(a)--improved Wilson quark simulations. We discuss the evidence of the onset of chiral logarithms in the pion decay constant. An overview is given of current extrapolation…

High Energy Physics - Lattice · Physics 2007-05-23 S. V. Wright