相关论文: Overlap Dirac Operator, Eigenvalues and Random Mat…
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…
This introductory presentation describes the Overlap Dirac Operator, why it could be useful in numerical QCD, and how it can be implemented.
We propose new techniques to implement numerically the overlap-Dirac operator which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger model and the…
We propose new techniques for the numerical implementation of the overlap-Dirac operator, which exploit the physical properties of the underlying theory to avoid nested algorithms. We test these procedures in the two-dimensional Schwinger…
Random matrix theory is a powerful way to describe universal correlations of eigenvalues of complex systems. It also may serve as a schematic model for disorder in quantum systems. In this review, we discuss both types of applications of…
We compute fermionic observables relevant to the study of chiral symmetry in quenched QCD using the Overlap-Dirac operator for a wide range of the fermion mass. We use analytical results to disentangle the contribution from exact zero modes…
Random matrix theory and chiral Lagrangians offer a convenient tool for the exact calculation of microscopic spectral correlators of the Dirac operator in a well-defined finite-volume scaling regime.
In this talk we present the results published recently in Ref. [1], where we showed how to introduce a quark chemical potential in the overlap Dirac operator. The resulting operator satisfies a Ginsparg-Wilson relation and has exact zero…
We summarize our recent investigations of lattice QCD with dynamical overlap fermions. We sketch algorithmic issues and our approach to solving them. We show our measurement of the topological susceptibility. We describe a computation of…
We show that, with an appropriate choice of a Dirac operator, there is a remnant of chiral anomalies in the reduced model in which there is no coordinate dependences of the gauge field. This result is obtained by exploring a topological…
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 have computed ensembles of complete spectra of the staggered Dirac operator using four-dimensional SU(2) gauge fields, both in the quenched approximation and with dynamical fermions. To identify universal features in the Dirac spectrum,…
The aim of the lectures is to introduce first-year Ph.D. students and research workers to the theory of the Dirac operator, spinor techniques, and their relevance for the theory of eigenvalues in Riemannian geometry. Topics: differential…
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 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…
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…
Exact results from random matrix theory are used to systematically analyse the relationship between microscopic Dirac spectra and finite-volume partition functions. Results are presented for the unitary ensemble, and the chiral analogs of…
The chiral Jacobian, which is defined with Neuberger's overlap Dirac operator of the lattice fermion, is explicitly evaluated in the continuum limit without expanding it in the gauge coupling constant. Our calculational scheme is simple and…
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…
After a brief introduction to the overlap two examples relating to topological properties of chiral fermion systems in interaction with gauge fields are presented: It is shown how the overlap preserves the continuum structure of exact…