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

Optical Production of Stable Ultracold 88^{88}Sr2_2 Molecules

We have produced large samples of ultracold $^{88}$Sr$_2$ molecules in the electronic ground state in an optical lattice. The molecules are bound by 0.05 cm$^{-1}$ and are stable for several milliseconds. The fast, all-optical method of molecule creation via intercombination line photoassociation relies on a near-unity Franck-Condon factor. The detection uses a weakly bound vibrational level corresponding to a very large dimer. This is the first of two steps needed to create Sr$_2$ in the absolute ground quantum state. Lattice-trapped Sr$_2$ is of interest to frequency metrology and ultracold chemistry.Comment: 5 pages, 3 figure

Useful Descriptions of Organizational Processes: Collecting Data for the Process Handbook

This paper describes a data collection methodology for business process analysis. Unlike static objects, business processes are semi-repetitive sequences of events that are often widely distributed in time and space, with ambiguous boundaries. To redesign or even just describe a business process requires an approach that is sensitive to these aspects of the phenomena. The method described here is intended to generate semi-formal process representations suitable for inclusion in a "handbook" of organizational processes. Using basic techniques of ethnographic interviewing and observation, the method helps users map decomposition, specialization, and dependency relationships at an intermediate level of abstraction meaningful to participants. By connecting new process descriptions to an existing taxonomy of similar descriptions in the Handbook, this method helps build a common vocabulary for process description and analysis.

Stochastic field theory for a Dirac particle propagating in gauge field disorder

Recent theoretical and numerical developments show analogies between quantum chromodynamics (QCD) and disordered systems in condensed matter physics. We study the spectral fluctuations of a Dirac particle propagating in a finite four dimensional box in the presence of gauge fields. We construct a model which combines Efetov's approach to disordered systems with the principles of chiral symmetry and QCD. To this end, the gauge fields are replaced with a stochastic white noise potential, the gauge field disorder. Effective supersymmetric non-linear sigma-models are obtained. Spontaneous breaking of supersymmetry is found. We rigorously derive the equivalent of the Thouless energy in QCD. Connections to other low-energy effective theories, in particular the Nambu-Jona-Lasinio model and chiral perturbation theory, are found.Comment: 4 pages, 1 figur

Calorons and localization of quark eigenvectors in lattice QCD

We analyze the localization properties for eigenvectors of the Dirac operator in quenched lattice QCD in the vicinity of the deconfinement phase transition. Studying the characteristic differences between the Z_3 sectors above the critical temperature T_c, we find indications for the presence of calorons.Comment: 4 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

Renormalization Group and Infinite Algebraic Structure in D-Dimensional Conformal Field Theory

We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations. In the fixed point the diffeomorphism and Weyl transformations generate an infinite algebraic structure of D-Dimensional conformal field theory models. The Wilson expansion and crossing symmetry enable to obtain sum rules for dimensions of composite operators and Wilson coefficients.Comment: 16 page

Adaptive multigrid algorithm for the lattice Wilson-Dirac operator

We present an adaptive multigrid solver for application to the non-Hermitian Wilson-Dirac system of QCD. The key components leading to the success of our proposed algorithm are the use of an adaptive projection onto coarse grids that preserves the near null space of the system matrix together with a simplified form of the correction based on the so-called gamma_5-Hermitian symmetry of the Dirac operator. We demonstrate that the algorithm nearly eliminates critical slowing down in the chiral limit and that it has weak dependence on the lattice volume