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Philippe de Forcrand

Publications and source records attributed to Philippe de Forcrand.

115 records · Page 7Linked to original sources
arXiv1995

Systematic errors of Lüscher's fermion method and its extensions

We study the systematic errors of Lüscher's formulation of dynamical Wilson quarks and some of its variants, in the weak and strong coupling limits, and on a sample of small configurations at finite $β$. We confirm the existence of an optimal window in the cutoff parameter $\varepsilon$, and the exponential decrease of the error with the number of boson families. A non-hermitian variant improves the approximation further and allows for an odd number of flavors. A simple and economical Metropolis test is proposed, which makes the algorithm exact.

hep-lat↗
arXiv1994

The continuum limit of the lattice Gribov problem, and a solution based on Hodge decomposition

We study gauge fixing via the standard local extremization algorithm for 2-dimensional $U(1)$. On a lattice with spherical topology $S^2$ where all copies are lattice artifacts, we find that the number of these 'Gribov' copies diverges in the continuum limit. On a torus, we show that lattice artifacts can lead to the wrong evaluation of the gauge-invariant correlation length, when measured via a gauge-fixed procedure; this bias does not disappear in the continuum limit. We then present a new global approach, based on Hodge decomposition of the gauge field, which produces a unique smooth field in Landau gauge, and is economically powered by the FFT. We also discuss the use of this method for examining topological objects, and its extensions to non-abelian gauge fields.

hep-lat↗
arXiv1994

Fast Krylov Space Methods for Calculation of Quark Propogator

Different recently developed Krylov space methods for solving linear systems are studied and compared for the solution of the Dirac equation on the lattice. Stabilized Biconjugate Gradient (BiCGstab2) is shown to be a robust and efficient solver for the calculation of the Wilson quark propagator in lattice QCD.

hep-lat↗
arXiv1992

Glueball wavefunctions

We measure Coulomb-gauge wavefunctions of the scalar and tensor glueballs in SU(2) Yang-Mills. The problem of contamination by flux states is discussed, and a new analysis method described. The large size of the tensor glueball is confirmed. Preliminary results in the deconfined phase show no significant changes.

hep-lat↗
arXiv1992

The fermion sign problem: A new decoupling transformation, and a new simulation algorithm

We discuss the Fermion sign problem and, by examining a very general Hubbard-Stratonovich (HS) transformation, argue that the sign problem cannot be solved with such methods. We propose a different kind of transformation which, while not solving the sign problem, shows more detailed information about the system. With our transformation it is {\it trivial} to tell which auxiliary field configurations give a positive sign and which give a negative sign. We then discuss briefly various properties of this transformation and construct a new algorithm which with one simulation gives results for a whole range of particle densities and Hubbard $U$ values, positive and negative. Our approach is in excellent agreement with exact calculations.

cond-mat↗
arXiv1992

Nonperturbative evaluation of the diffusion rate in field theory at high temperatures

Kramer's approach to the rate of the thermally activated escape from a metastable state is extended to field theory. Diffusion rate in the 1+1-dimensional Sine-Gordon model as a function of temperature and friction coefficient is evaluated numerically by solving the Langevin equation in real time. A clear crossover from the semiclassical to the high temperature domain is observed. The temperature behaviour of the diffusion rate allows one to determine the kink mass which is found equal to the corresponding classical value. The Kramer's predictions for the dependence on viscosity are qualitatively valid in this multidimensional case. In the limit of vanishing friction the diffusion rate is shown to coincide with the one obtained from the direct measurements of the conventional classical real-time Green function at finite temperature.

hep-lat↗