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Universal Behavior in Dirac Spectra
J. J. M. Verbaarschot
In these lectures we review recent results on universal fluctuations of QCD Dirac spectra and applications of Random Matrix Theory (RMT) to QCD. We review general properties of Dir…
Random-matrix universality in the small-eigenvalue spectrum of the lattice Dirac operator
M. E. Berbenni-Bitsch, A. D. Jackson, S. Meyer +3
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.…
Universal Fluctuations in Dirac Spectra
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…
Chiral symmetry and the spectrum of the QCD Dirac operator
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 t…
Universality of Correlation Functions in Random Matrix Models of QCD
A. D. Jackson, M. K. Sener, J. J. M. Verbaarschot
We demonstrate the universality of the spectral correlation functions of a QCD inspired random matrix model that consists of a random part having the chiral structure of the QCD Di…
Microscopic universality in the spectrum of the lattice Dirac operator
M. E. Berbenni-Bitsch, S. Meyer, A. Schäfer +2
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…
Random matrix triality at nonzero chemical potential
M. A. Halasz, J. C. Osborn, J. J. M. Verbaarschot
We introduce three universality classes of chiral random matrix ensembles with a nonzero chemical potential and real, complex or quaternion real matrix elements. In the thermodynam…
Fermion determinants in matrix models of QCD at nonzero chemical potential
M. A. Halasz, A. D. Jackson, J. J. M. Verbaarschot
The presence of a chemical potential completely changes the analytical structure of the QCD partition function. In particular, the eigenvalues of the Dirac operator are distributed…