Equivalent of a Thouless energy in lattice QCD Dirac spectra

Random matrix theory (RMT) is a powerful statistical tool to model spectral fluctuations. In addition, RMT provides efficient means to separate different scales in spectra. Recently RMT has found application in quantum chromodynamics (QCD). In mesoscopic physics, the Thouless energy sets the universal scale for which RMT applies. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator with staggered fermions and $SU_c(2)$ lattice gauge fields. Comparing lattice data with RMT predictions we find deviations which allow us to give an estimate for this scale.Comment: LATTICE99 (theor. devel.), 3 pages, 4 figure

Universal and non-universal behavior in Dirac spectra

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, we compare the lattice data with predictions from chiral random matrix theory for the distribution of the low-lying eigenvalues. Good agreement is found up to some limiting energy, the so-called Thouless energy, above which random matrix theory no longer applies. We determine the dependence of the Thouless energy on the simulation parameters using the scalar susceptibility and the number variance.Comment: LATTICE98(confine), 9 pages, 11 figure

Kramers Equation Algorithm with Kogut-Susskind Fermions on Lattice

We compare the performance of the Kramers Equation Monte Carlo (KMC) Algorithm with that of the Hybrid Monte Carlo (HMC) algorithm for numerical simulations with dynamical Kogut-Susskind fermions. Using the lattice Gross-Neveu model in 2 space-time dimensions, we calculate the integrated autocorrelation time of different observables at a number of couplings in the scaling region on 16^2 and 32^2 lattices while varying the parameters of the algorithms for optimal performance. In our investigation the performance of KMC is always significantly below than that of HMC for the observables used. We also stress the importance of having a large number of configurations for the accurate estimation of the integrated autocorrelation time.Comment: revised version to appear in Phys. Lett. B, 9 pages, 3 ps figure

FFT modelling of high resolution XRD peaks with a discrete Green operator and a sub-voxelization method

International audienceSynchrotron X-ray now allows to study in situ and in real time the mechanical behavior of materials under loading and/or phase transformation. Such experiments result in thousands 2D diffraction patterns. However, the analysis of these images is not an easy task because they are sensitive to microstructural defects, internal stresses and applied load. An alternative method to complete this study is the forward modeling of the diffraction patterns. In this numerical method, we first need to compute the mechanical fields (strain or displacement fields) in a deformed material. The computed field is then used to generate theoretical X-ray diffraction peaks, which are compared to experimental results. The quality of the forward modeling method strongly depends on the accuracy of the numerical method used to compute the mechanical fields. In the present paper, a micromechanical method based on the FFT algorithm is used to compute the displacement field. To improve this spectral method, we develop a discrete Green operator to suppress numerical oscillations and a sub-voxelization method to remove artifacts on the displacement field. Throughout numerical examples, we show the effect of these numerical defects on the simulated peaks and finally our numerical model is used to study some reference cases such as perfect or faulted dislocation loops, or a random distribution of dislocation loops.La construction de sources synchrotron de rayons X a permis l'étude in situ et en temps réel des matériaux sous chargements mécaniques et/ou transformation de phase. Ces expériences produisent des milliers de diagrammes de diffraction 2D dont l'analyse n'est pas triviale car elles résultent de l'effet conjugué des défauts microstructuraux, des contraintes internes et des chargements mécaniques. La modélisation numérique des diagrammes de diffraction est donc nécessaire. Elle consiste à évaluer les champs mécaniques (champs de déformations ou de déplacements) dans un matériau et à générer les diagrammes théoriques correspondant à cet état de contraintes. La précision de cette modélisation est liée à celle de la méthode numérique utilisée pour calculer les champs mécaniques. Pour simuler les diagrammes théoriques, nous utilisons une méthode micromécanique basée sur l'algorithme FFT pour calculer le champ de déplacements dans un matériau de structure périodique. Pour améliorer la précision de cette méthode, nous introduisons un opérateur de Green discret et une méthode de sous-voxélisation pour la suppression des oscillations numériques et des artéfacts numériques. Nous montrons l'effet de ces défauts numériques sur les diagrammes de diffraction et appliquons le modèle pour étudier des cas de référence comme des boucles de dislocations parfaites et partielles, ou encore une répartition aléatoire de boucles de dislocations

Can we do better than Hybrid Monte Carlo in Lattice QCD?

The Hybrid Monte Carlo algorithm for the simulation of QCD with dynamical staggered fermions is compared with Kramers equation algorithm. We find substantially different autocorrelation times for local and nonlocal observables. The calculations have been performed on the parallel computer CRAY T3D.Comment: Talk presented at LATTICE96(algorithms), LaTeX 3 pages, uses espcrc2, epsf, 2 postscript figure

A FFT-based approach for Mesoscale Field Dislocation Mechanics: application to grain size effect in polycrystals

International audienceA crystal elasto-viscoplastic FFT formulation coupled with the Mesoscale Field Dislocation Mechanics (MFDM) theory is presented. This MFDM-EVPFFT approach accounts for plastic flow and hardening from densities of geometrically necessary dislocations (GND) in addition to statistically stored dislocations (SSD). It is shown on 3D periodic Voronoi polycrystals that GND densities modify both intra-granular incompatible fields and stresses, which are at the origin of a grain size dependent flow stress of the Hall-Petch type

Random Matrix Theory, Chiral Perturbation Theory, and Lattice Data

Recently, the chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that the deviations of lattice results from random matrix theory starting around the so-called Thouless energy can be understood in terms of chiral perturbation theory as well. Comparison of lattice data with chiral perturbation theory formulae allows us to compute the pion decay constant. We present results from a calculation for quenched SU(2) with Kogut-Susskind fermions at \beta=2.0 and 2.2.Comment: LaTeX, 12 pages, 7 .eps figure

Beyond the Thouless energy

The distribution and the correlations of the small eigenvalues of the Dirac operator are described by random matrix theory (RMT) up to the Thouless energy $E_c\propto 1/\sqrt{V}$, where $V$ is the physical volume. For somewhat larger energies, the same quantities can be described by chiral perturbation theory (chPT). For most quantities there is an intermediate energy regime, roughly $1/V<E<1/\sqrt{V}$, where the results of RMT and chPT agree with each other. We test these predictions by constructing the connected and disconnected scalar susceptibilities from Dirac spectra obtained in quenched SU(2) and SU(3) simulations with staggered fermions for a variety of lattice sizes and coupling constants. In deriving the predictions of chPT, it is important to take into account only those symmetries which are exactly realized on the lattice.Comment: LATTICE99(Theoretical Developments), 3 pages, 3 figures, typo in Ref. [10] correcte

Random Matrix Theory and Chiral Logarithms

Recently, the contributions of chiral logarithms predicted by quenched chiral perturbation theory have been extracted from lattice calculations of hadron masses. We argue that a detailed comparison of random matrix theory and lattice calculations allows for a precise determination of such corrections. We estimate the relative size of the m*log(m), m, and m^2 corrections to the chiral condensate for quenched SU(2).Comment: LaTeX (elsart.cls), 9 pages, 6 .eps figures, added reference, altered discussion of Eq.(9