Probing the QCD Vacuum with Static Sources in Maximal Abelian Projection

Various field strength correlators are investigated in the maximal Abelian projection of pure SU(2) lattice gauge theory. High precision measurements of the colour fields, monopole currents, their curls and divergences allow for detailed checks of the dual superconductor scenario. On this basis, we perform a Ginzburg-Landau type analysis of the flux tube profile from which we derive the size of the penetration length, LAMBDA = 0.16(2) fm, and coherence length of the monopole condensate wave function, XI = 0.27(3) fm. The ratio of these numbers is KAPPA = LAMBDA/XI = 0.59(13) which is below the value 1/SQRT(2) where type II superconductivity sets in.Comment: 15 pages, latex, 8 figures, Talk presented by K. Schilling YKIS97, Kyot

Many Masses on One Stroke: Economic Computation of Quark Propagators

The computational effort in the calculation of Wilson fermion quark propagators in Lattice Quantum Chromodynamics can be considerably reduced by exploiting the Wilson fermion matrix structure in inversion algorithms based on the non-symmetric Lanczos process. We consider two such methods: QMR (quasi minimal residual) and BCG (biconjugate gradients). Based on the decomposition $M/\kappa={\bf 1}/\kappa-D$ of the Wilson mass matrix, using QMR, one can carry out inversions on a {\em whole} trajectory of masses simultaneously, merely at the computational expense of a single propagator computation. In other words, one has to compute the propagator corresponding to the lightest mass only, while all the heavier masses are given for free, at the price of extra storage. Moreover, the symmetry $\gamma_5\, M= M^{\dagger}\,\gamma_5$ can be used to cut the computational effort in QMR and BCG by a factor of two. We show that both methods then become---in the critical regime of small quark masses---competitive to BiCGStab and significantly better than the standard MR method, with optimal relaxation factor, and CG as applied to the normal equations.Comment: 17 pages, uuencoded compressed postscrip

Anatomy of String Breaking in QCD

We investigate the string breaking mechanism in n_f=2 QCD. We discuss the lattice techniques used and present results on energy levels and mixing angle of the static BBbar|QbarQ two-state system. The string breaking is visualized, by means of an animation of the action density distribution as a function of the static colour source-antisource separation.Comment: Talk presented at Lattice 2005 (Topology and Confinement), Dublin, July 25-30, 2005; 6 pages, 5 figures, 2 mpeg animations not included because of file size problems but href linked, uses PoS.cls; to appear in Proceedings of Scienc

Finite size scaling analysis of compact QED

We describe results of a high-statistics finite size scaling analysis of 4d compact U(1) lattice gauge theory with Wilson action at the phase transition point. Using a multicanonical hybrid Monte Carlo algorithm we generate data samples with more than 150 tunneling events between the metastable states of the system, on lattice sizes up to 18^4. We performed a first analysis within the Borgs-Kotecky finite size scaling scheme. As a result, we report evidence for a first-order phase transition with a plaquette energy gap, G=0.02667(20), at a transition coupling, beta_T=1.011128(11).Comment: Lattice 2000 (Topics in Gauge Theories),6 pages, 6 figures, LaTe

Spatial Besov Regularity for Stochastic Partial Differential Equations on Lipschitz Domains

We use the scale of Besov spaces B^\alpha_{\tau,\tau}(O), \alpha>0, 1/\tau=\alpha/d+1/p, p fixed, to study the spatial regularity of the solutions of linear parabolic stochastic partial differential equations on bounded Lipschitz domains O\subset R^d. The Besov smoothness determines the order of convergence that can be achieved by nonlinear approximation schemes. The proofs are based on a combination of weighted Sobolev estimates and characterizations of Besov spaces by wavelet expansions.Comment: 32 pages, 3 figure