Related papers: Fun with Dirac eigenvalues
We summarize recent analytical results obtained for lattice artifacts of the non-Hermitian Wilson Dirac operator. Hereby we discuss the effect of all three low energy constants. In particular we study the limit of small lattice spacing and…
In this lecture we review recent lattice QCD studies of the statistical properties of the eigenvalues of the QCD Dirac operator. We find that the fluctuations of the smallest Dirac eigenvalues are described by chiral Random Matrix Theories…
Several lattice calculations which probe the chiral and topological structure of QCD are discussed. The results focus attention on the low-lying eigenmodes of the Dirac operator in typical gauge field configurations.
We analyze the smallest Dirac eigenvalues by formulating an effective theory for the QCD Dirac spectrum. We find that in a domain where the kinetic term of the effective theory can be ignored, the Dirac eigenvalues are distributed according…
The distribution of individual Dirac eigenvalues is derived by relating them to the density and higher eigenvalue correlation functions. The relations are general and hold for any gauge theory coupled to fermions under certain conditions…
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…
We discuss the behaviour of the spectral density of the massless Dirac operator at the small eigenvalues and quark masses compatible with the restrictions imposed by the low energy theorems in QCD. Sum rule for its derivative over the quark…
We analyze the low-lying spectrum and eigenmodes of lattice Dirac operators with a twisted mass term. The twist term expels the eigenvalues from a strip in the complex plane and all eigenmodes obtain a non-vanishing matrix element with…
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…
The eigenvalue spectrum $\rho(\lambda)$ of the Dirac operator is numerically calculated in lattice QCD with 2+1 flavors of dynamical domain-wall fermions. In the high-energy regime, the discretization effects become significant. We subtract…
The spectral flow of the low-lying eigenvalues of the improved and unimproved Wilson-Dirac operator is studied on instanton-like configurations and on thermalized quenched configurations at various $\beta$-values and lattice sizes. We also…
We get optimal lower bounds for the eigenvalues of the submanifold Dirac operator on locally reducible Riemannian manifolds in terms of intrinsic and extrinsic expressions. The limiting-cases are also studied. As a corollary, one gets…
Measurements of the lowest-lying eigenvalues of the staggered fermion Dirac operator are made on ensembles of equilibrium gauge field configurations in quenched SU(3) lattice gauge theory. The results are compared with exact analytical…
With the Schwinger model as example I discuss properties of lattice Dirac operators, with some emphasis on Monte Carlo results for topological charge, chiral fermions and eigenvalue spectra.
We investigate several aspects of the nodal geometry and topology of Laplace eigenfunctions, with particular emphasis on the low frequency regime. This includes investigations in and around the Payne property, opening angle estimates of…
The magnetic Dirac operator describes the relativistic motion of a charged particle in a magnetic field. Although this operator got a lot of attention in physics many of its fundamental mathematical properties remain unexplored and this…
We have calculated complete spectra of the staggered Dirac operator on the lattice in quenched SU(3) gauge theory for \beta = 5.4 and various lattice sizes. The microscopic spectral density, the distribution of the smallest eigenvalue, and…
We compare the low-lying spectrum of the staggered Dirac operator in the confining phase of compact U(1) gauge theory on the lattice to predictions of chiral random matrix theory. The small eigenvalues contribute to the chiral condensate…
We prove a lower bound for the first eigenvalue of the Dirac operator on a compact Riemannian spin manifold depending on the scalar curvature as well as a chosen Codazzi tensor. The inequality generalizes the classical estimate from [2].
We study the eigenvalue spectrum of different lattice Dirac operators (staggered, fixed point, overlap) and discuss their dependence on the topological sectors. Although the model is 2D (the Schwinger model with massless fermions) our…