Related papers: Universal Behavior in Dirac Spectra

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…

We use the graded eigenvalue method, a variant of the supersymmetry technique, to compute the universal spectral correlations of the QCD Dirac operator in the presence of massive dynamical quarks. The calculation is done for the chiral…

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…

These notes are based on the lectures delivered at the Les Houches Summer School in July 2015. They are addressed at a mixed audience of physicists and mathematicians with some basic working knowledge of random matrix theory. The first part…

We apply the complex Langevin (CL) method to a chiral random matrix theory (ChRMT) at non-zero chemical potential and study the nearest neighbor spacing (NNS) distribution of the Dirac eigenvalues. The NNS distribution is extracted using an…

The relation between the spectral density of the QCD Dirac operator at nonzero baryon chemical potential and the chiral condensate is investigated. We use the analytical result for the eigenvalue density in the microscopic regime which…

The importance of the spectral density of the Dirac operator in studying spontaneous chiral symmetry breaking and anomalous U(1) axial symmetry breaking are reviewed. It is shown that both types of symmetry breaking can be traced to effects…

We examine random matrix models of QCD which are capable of supporting both chiral and diquark condensation. A numerical study of the spectral densities near zero virtuality shows that the introduction of color in the interactions does not…

Random matrix theory (RMT) provides a powerful framework for analyzing universal features of strongly coupled physical systems. In quantum chromodynamics (QCD), cold quark matter at asymptotically high density is expected to exhibit color…

We use a chiral random matrix model with 2N_f flavors to mock up the QCD Dirac spectrum at finite chemical potential. We show that the 1/N approximation breaks down in the quenched state with spontaneously broken chiral symmetry. The…

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor…

For QCD at non-zero chemical potential $\mu$, the Dirac eigenvalues are scattered in the complex plane. We define a notion of ordering for individual eigenvalues in this case and derive the distributions of individual eigenvalues from…

Spontaneous chiral symmetry breaking in QCD with massless quarks at infinite volume can be seen in a finite box by studying, for instance, the dependence of the chiral condensate from the volume and the quark mass. We perform a feasibility…

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…

In this paper the kernel for the spectral correlation functions of the invariant chiral random matrix ensembles with real ($\beta =1$) and quaternion real ($\beta = 4$) matrix elements is expressed in terms of the kernel of the…

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…

I shall present a proof of universality of the microscopic spectral correlations in Verbaarschot's random matrix models of QCD, to corroborate the beautiful agreement between the predictions from the gaussian model and the numerical data.…

We study universal traits which emerge both in real-world complex datasets, as well as in artificially generated ones. Our approach is to analogize data to a physical system and employ tools from statistical physics and Random Matrix Theory…

A chiral random matrix model with complex eigenvalues is solved as an effective model for QCD with non-vanishing chemical potential. We derive new matrix model correlation functions which predict the local fluctuations of complex Dirac…

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…