Comparing lattice Dirac operators with Random Matrix Theory

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 observations indicate possible problems in 4D applications. In particular misidentification of the smallest eigenvalues due to non-identification of the topological sector may hinder successful comparison with Random Matrix Theory (RMT).Comment: LATTICE99(topology and confinement), Latex2e using espcrc2.sty, 3 pages, 3 figure

Statistical analysis and the equivalent of a Thouless energy in lattice QCD Dirac spectra

Random Matrix Theory (RMT) is a powerful statistical tool to model spectral fluctuations. This approach has also found fruitful application in Quantum Chromodynamics (QCD). Importantly, RMT provides very efficient means to separate different scales in the spectral fluctuations. We try to identify the equivalent of a Thouless energy in complete spectra of the QCD Dirac operator for staggered fermions from SU(2) lattice gauge theory for different lattice size and gauge couplings. In disordered systems, the Thouless energy sets the universal scale for which RMT applies. This relates to recent theoretical studies which suggest a strong analogy between QCD and disordered systems. The wealth of data allows us to analyze several statistical measures in the bulk of the spectrum with high quality. We find deviations which allows us to give an estimate for this universal scale. Other deviations than these are seen whose possible origin is discussed. Moreover, we work out higher order correlators as well, in particular three--point correlation functions.Comment: 24 pages, 24 figures, all included except one figure, missing eps file available at http://pluto.mpi-hd.mpg.de/~wilke/diff3.eps.gz, revised version, to appear in PRD, minor modifications and corrected typos, Fig.4 revise

Spectrum of the fixed point Dirac operator in the Schwinger model

Recently, properties of the fixed point action for fermion theories have been pointed out indicating realization of chiral symmetry on the lattice. We check these properties by numerical analysis of the spectrum of a parametrized fixed point Dirac operator investigating also microscopic fluctuations and fermion condensation.Comment: LATTICE98(improvement), 3 pages, 3 figure

Fake symmetry transitions in lattice Dirac spectra

In a recent lattice investigation of Ginsparg-Wilson-type Dirac operators in the Schwinger model, it was found that the symmetry class of the random matrix theory describing the small Dirac eigenvalues appeared to change from the unitary to the symplectic case as a function of lattice size and coupling constant. We present a natural explanation for this observation in the framework of a random matrix model, showing that the apparent change is caused by the onset of chiral symmetry restoration in a finite volume. A transition from unitary to symplectic symmetry does not occur.Comment: 6 pages, 3 figures, REVTe

A Presence- and Performance-Driven Framework to Investigate Interactive Networked Music Learning Scenarios

Cooperative music making in networked environments has been subject of extensive research, scientific and artistic. Networked music performance (NMP) is attracting renewed interest thanks to the growing availability of effective technology and tools for computer-based communications, especially in the area of distance and blended learning applications. We propose a conceptual framework for NMP research and design in the context of classical chamber music practice and learning: presence-related constructs and objective quality metrics are used to problematize and systematize the many factors affecting the experience of studying and practicing music in a networked environment. To this end, a preliminary NMP experiment on the effect of latency on chamber music duos experience and quality of the performance is introduced. The degree of involvement, perceived coherence, and immersion of the NMP environment are here combined with measures on the networked performance, including tempo trends and misalignments from the shared score. Early results on the impact of temporal factors on NMP musical interaction are outlined, and their methodological implications for the design of pedagogical applications are discussed

Modélisation et simulation numérique par méthode FFT de la localisation des contraintes internes et des densités de dislocations dans un acier composite nouvelle génération 'Fe-TiB2'

International audienceUn modèle d'élasto-viscoplasticité cristalline (EVP), basé sur la méthode des transformées de Fourier rapide (FFT) et couplé à la mécanique des champs de dislocations (MFDM), est présenté et appliqué afin de décrire l'évolution en déformation des densités de Dislocations Géométriques Nécessaires (GND) dans un composite à matrice métallique Fe-TiB2. Des volumes élémentaires réalistes basés sur la microstructure réelle sont considérés. Les résultats montrent la capacité de l'approche à prédire les gradients des champs mécaniques proches des interfaces matrice/renforts

Spectrum of the U(1) staggered Dirac operator in four dimensions

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 similar as for the SU(2) and SU(3) gauge groups. Agreement with the chiral unitary ensemble is observed below the Thouless energy, which is extracted from the data and found to scale with the lattice size according to theoretical predictions.Comment: 5 pages, 3 figure

Zaltoprofen/4,4′-Bipyridine: A Case Study to Demonstrate the Potential of Differential Scanning Calorimetry (DSC) in the Pharmaceutical Field

The Zaltoprofen/4,4′-Bipyridine system gives rise to two co-crystals of different compositions both endowed - in water and in buffer solution at pH 4.5 - with considerably higher solubility and dissolution rate than the pure drug. The qualitative and quantitative analysis of the DSC measurements, carried out on samples made up of mixtures prepared according to different methodologies, allows us to elaborate and propose an accurate thermodynamic model that fully takes into account the qualitative aspects of the complex experimental framework and which provides quantitative predictions (reaction enthalpies and compositions of the co-crystals) in excellent agreement with the experimental results. Co-crystal formation and cocrystal compositions were confirmed by X-ray diffraction measurements as well as by FT-IR and NMR spectroscopy measurements. The quantitative processing of DSC measurements rationalizes and deepens the scientific aspects underlying the so-called Tammann's triangle and constitutes a model of general validity. The work shows that DSC has enormous potential, which however can be fully exploited only by paying adequate attention to the experimental aspects and the quantitative processing of the measurements

Universal Scaling of the Chiral Condensate in Finite-Volume Gauge Theories

We confront exact analytical predictions for the finite-volume scaling of the chiral condensate with data from quenched lattice gauge theory simulations. Using staggered fermions in both the fundamental and adjoint representations, and gauge groups SU(2) and SU(3), we are able to test simultaneously all of the three chiral universality classes. With overlap fermions we also test the predictions for gauge field sectors of non-zero topological charge. Excellent agreement is found in most cases, and the deviations are understood in the others.Comment: Expanded discussion of overlap fermion results. 17 pages revtex, 7 postscript figure

Staggered Fermions and Gauge Field Topology

Based on a large number of smearing steps, we classify SU(3) gauge field configurations in different topological sectors. For each sector we compare the exact analytical predictions for the microscopic Dirac operator spectrum of quenched staggered fermions. In all sectors we find perfect agreement with the predictions for the sector of topological charge zero, showing explicitly that the smallest Dirac operator eigenvalues of staggered fermions at presently realistic lattice couplings are insensitive to gauge field topology. On the smeared configurations, $4\nu$ eigenvalues clearly separate out from the rest on configurations of topological charge $\nu$, and move towards zero in agreement with the index theorem.Comment: LaTeX, 10 page