Related papers: Spectral Density of the QCD Dirac Operator near Ze…
We use low lying eigenvectors of the overlap-Dirac operator as a probe of the QCD vacuum. If instantons play a significant role one would expect the low lying eigenmodes of the overlap-Dirac operator to consist mainly of the mixed ``would…
A formal fourth order differential operator with a singular coefficient that is a linear combination of the Dirac delta-function and its derivatives is considered. The asymptotic behavior of spectra and eigenfunctions of a family of…
Using general properties of the $Q=0$ topological sector we previously argued that a vector-like theory, with chiral $U(1)_A$ anomaly, and exact non-Abelian chiral symmetry, should exhibit divergent susceptibilities in the chiral limit, the…
Using operator methods, we generally present the level densities for kinds of random matrix unitary ensembles in weak sense. As a corollary, the limit spectral distributions of random matrices from Gaussian, Laguerre and Jacobi unitary…
Based on random matrix theory in the unitary ensemble, we derive the double-microscopic massive spectral correlators corresponding to the Dirac operator of QCD_3 with an even number of fermions N_f. We prove that these spectral correlators…
We compute by Monte Carlo methods the individual distributions of the $k$th smallest Dirac operator eigenvalues in QCD, and compare them with recent analytical predictions. We do this for both massless and massive quarks in an SU(3) gauge…
We present a quantitative analysis of the microscopic Dirac spectrum which is complex in the presence of a non-vanishing quark chemical potential. Data from quenched SU(3) lattice simulations for different volumes V and small values of the…
Applying the replica method of statistical mechanics, we evaluate the eigenvalue density of the large random matrix (sample covariance matrix) of the form $J = A^{\rm T} A$, where $A$ is an $M \times N$ real sparse random matrix. The…
We discuss the limiting spectral density of real symmetric random matrices. Other than in standard random matrix theory the upper diagonal entries are not assumed to be independent, but we will fill them with the entries of a stochastic…
We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…
We propose a new way of understanding how chiral symmetry is realized in the high temperature phase of QCD. Based on the finding that a simple free instanton gas precisely describes the details of the lowest part of the spectrum of the…
We define Dirac operators on $\mathbb{S}^3$ (and $\mathbb{R}^3$) with magnetic fields supported on smooth, oriented links and prove self-adjointness of certain (natural) extensions. We then analyze their spectral properties and show, among…
We study spectral properties of a one-dimensional Dirac equation with various disorder. We use replicas to calculate the exact density of state and typical localization length of a Dirac particle in several cases. We show that they can be…
We derive the mean eigenvalue density for symmetric Gaussian random N x N matrices in the limit of large N, with a constraint implying that the row sum of matrix elements should vanish. The result is shown to be equivalent to a result found…
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…
We exposit the eigenvalue distribution of the lattice Dirac operator in Quantum Chromodynamics with two colors (i.e. two-color QCD). We explicitly calculate all the eigenvalues in the presence of finite quark chemical potential \mu for a…
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…
We show that the spectrum of the Dirac operator in complex Langevin simulations of QCD at non-zero chemical potential must behave in a way which is radically different from the one in simulations with ordinary non-complexified gauge fields:…
We study characteristic features of the eigenvalues of the Wilson-Dirac operator in topologically non-trivial gauge field configurations by examining complete spectra of the fermion matrix. In particular we discuss the role of eigenvectors…
We examine the behavior of the spectral function for the trace of the stress tensor in QCD in the two regimes where it is possible to make analytical progress; weak coupling, and close to a second order QCD phase transition. We determine…