相关论文: Fun with Dirac eigenvalues
The low energy eigenmodes of the continuum QCD Dirac operator are extended, but on the lattice, due to discretization effects, the Dirac operator can have localized eigenmodes. These non-physical modes can introduce strong lattice artifacts…
We present a detailed study of the interplay between chiral symmetry and spectral properties of the Dirac operator in lattice gauge theories. We consider, in the framework of the Schwinger model, the fixed point action and a fermion action…
Many Lagrangians of physical theories can be expressed as eigenvalues of certain, relatively simple, matrices involving Dirac gamma matrices. We give concrete examples for Lagrangian corresponding to a point particle coupled to…
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 estimate the behavior of the generalized eigenfunctions of critical Dirac operators (which are Dirac operators with eigenfunctions and/or resonances for $E=m$) plus small perturbations in the potential. The results also apply for other…
We investigate the eigenvalues of nearly chiral lattice Dirac operators constructed with five-dimensional implementations. Allowing small violation of the Ginsparg-Wilson relation, the HMC simulation is made much faster while the…
We compare eigenvalue correlations of the Dirac operator with a chemical potential obtained from lattice simulations of quenched QCD with analytic predictions obtained from chiral effective theories in the zero-momentum limit. By comparing…
We prove upper and lower bounds for the eigenvalues of the Dirac operator and the Laplace operator on 2-dimensional tori. In particluar we give a lower bound for the first eigenvalue of the Dirac operator for non-trivial spin structures. It…
Based on the exact relationship to Random Matrix Theory, we derive the probability distribution of the k-th smallest Dirac operator eigenvalue in the microscopic finite-volume scaling regime of QCD and related gauge theories.
We compare the behavior of different lattice Dirac operators in gauge backgrounds which are lattice discretizations of a classical instanton. In particular we analyze the standard Wilson operator, a chirally improved Dirac operator and the…
We derive an analytical expression for the distribution of the k-th smallest Dirac eigenvalue in QCD with imaginary isospin chemical potential in the Dirac operator. Because of its dependence on the pion decay constant F through the…
We exploit the connection between quantum dot Dirac operators and $\overline\partial$-Robin Laplacians. First, we find a graphical relation between their smallest positive eigenvalues, which allows us to deduce a recipe for translating…
We prove a new upper bound for the smallest eigenvalues of the Dirac operator on a compact hypersurface of the hyperbolic space.
The spectrum of low-lying eigenvalues of overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition…
We study localization and chirality properties of eigenvectors of the lattice Dirac operator. In particular we focus on the dependence of our observables on the size of the corresponding eigenvalue, which allows us to study the transition…
In this article, we consider the Dirac operator with constant magnetic field in $\mathbb R^2$. Its spectrum consists of eigenvalues of infinite multiplicities, known as the Landau-Dirac levels. Under compactly supported perturbations, we…
Low energy precision experiments provide significant tests of the laws of nature that can reveal physics beyond the Standard Model. A good theoretical understanding of the low energy properties of QCD is required for this purpose. The…
In this note, we prove lower and upper bounds for Dirac operators of submanifolds in certain ambient manifolds in terms of conformal and extrinsic quantities.
We show how the leading physical and Wilson low-energy constants associated with Wilson fermions in lattice gauge theory can be determined individually by using spectral information of the Wilson Dirac operator with fixed index at finite…
This review is devoted to the study of stationary solutions of linear and nonlinear equations from relativistic quantum mechanics, involving the Dirac operator. The solutions are found as critical points of an energy functional. Contrary to…