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I explain the concept that light quarks diffuse in the QCD vacuum following the spontaneous breakdown of chiral symmetry. I exploit the striking analogy to disordered electrons in metals, identifying, among others, the universal regime…

High Energy Physics - Phenomenology · Physics 2007-05-23 Maciej A. Nowak

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

We prove that QCD in the epsilon-regime of chiral Perturbation Theory is equivalent to chiral Random Matrix Theory for zero and both non-zero real and imaginary chemical potential mu. To this aim we prove a theorem that relates integrals…

High Energy Physics - Theory · Physics 2008-11-26 Francesco Basile , Gernot Akemann

In a deep-infrared (ergodic) regime, QCD coupled to massive pseudoreal and real quarks are described by chiral orthogonal and symplectic ensembles of random matrices. Using this correspondence, general expressions for the QCD partition…

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

We derive the hole probability and the distribution of the smallest eigenvalue of chiral hermitian random matrices corresponding to Dirac operators coupled to massive quarks in QCD. They are expressed in terms of the QCD partition function…

High Energy Physics - Theory · Physics 2016-08-25 S. M. Nishigaki , P. H. Damgaard , T. Wettig

We investigate the Dirac eigenvalue spectrum ($\rho(\lambda,m_l)$) to study the microscopic origin of axial anomaly in high temperature phase of QCD. We propose novel relations between the derivatives ($\partial^n \rho(\lambda,m_l)/\partial…

High Energy Physics - Lattice · Physics 2021-12-08 Heng-Tong Ding , Sheng-Tai Li , Swagato Mukherjee , Akio Tomiya , Xiao-Dan Wang , Yu Zhang

We argue that the spectrum of the QCD Dirac operator near zero virtuality can be described by random matrix theory. As in the case of classical random matrix ensembles of Dyson we have three distinct classes: the chiral orthogonal ensemble…

High Energy Physics - Theory · Physics 2011-07-18 Jacobus Verbaarschot

We summarise recent results for the chiral Random Two-Matrix Theory constructed to describe QCD in the epsilon-regime with imaginary chemical potential. The virtue of this theory is that unquenched Lattice simulations can be used to…

High Energy Physics - Theory · Physics 2008-11-26 G. Akemann

We construct a random matrix model that, in the large $N$ limit, reduces to the low energy limit of the QCD partition function put forward by Leutwyler and Smilga. This equivalence holds for an arbitrary number of flavors and any value of…

High Energy Physics - Theory · Physics 2016-09-06 E. V. Shuryak , J. J. M. Verbaarschot

We have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum,…

High Energy Physics - Lattice · Physics 2009-10-31 M. E. Berbenni-Bitsch , M. Göckeler , S. Meyer , A. Schäfer , T. Wettig

We review applications of random matrix theory to QCD at nonzero temperature and chemical potential. The chiral phase transition of QCD and QCD-like theories is discussed in terms of eigenvalues of the Dirac operator. We show that for QCD…

High Energy Physics - Phenomenology · Physics 2008-11-26 K. Splittorff , J. J. M. Verbaarschot

We model the QCD Dirac operator as a power-law random banded matrix (RBM) with the appropriate chiral symmetry. Our motivation is the form of the Dirac operator in a basis of instantonic zero modes with a corresponding gauge background of…

High Energy Physics - Theory · Physics 2009-11-10 Antonio M. Garcia-Garcia , James C. Osborn

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 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 introduce Random Matrix Models for the Hermitian Wilson-Dirac operator of QCD-like theories. We show that they are equivalent to the $\epsilon$-limit of the chiral Lagrangian for Wilson chiral perturbation theory. Results are obtained…

High Energy Physics - Lattice · Physics 2013-03-14 Mario Kieburg , Jacobus J. M. Verbaarschot , Savvas Zafeiropoulos

We present simulation results for lattice QCD with light pions. For the quark fields we apply chirally symmetric lattice Dirac operators, in particular the overlap hypercube operator, along with the standard overlap operator for comparison.…

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

Large ensembles of complete spectra of the Euclidean Dirac operator for staggered fermions are calculated for SU(2) lattice gauge theory. The accumulation of eigenvalues near zero is analyzed as a signal of chiral symmetry breaking and…

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

We link the spontaneous breakdown of chiral symmetry in Euclidean QCD to the collision of spectral shock waves in the vicinity of zero eigenvalue of Dirac operator. The mechanism, originating from complex Burger's-like equation for viscid,…

High Energy Physics - Phenomenology · Physics 2015-12-23 Jean-Paul Blaizot , Maciej A. Nowak , Piotr Warchoł

We investigate the eigenvalue spectrum of the staggered Dirac matrix in two-color QCD at nonzero temperature and at baryon density when the eigenvalues become complex. The quasi-zero modes and their role for chiral symmetry breaking and the…

High Energy Physics - Phenomenology · Physics 2007-05-23 Elmar Bittner , Maria-Paola Lombardo , Harald Markum , Rainer Pullirsch

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