The Yang-Mills vacuum in Coulomb gauge

The Yang-Mills Schr\"odinger equation is solved in Coulomb gauge for the vacuum by the variational principle using an ansatz for the wave functional, which is strongly peaked at the Gribov horizon. We find an infrared suppressed gluon propagator, an infrared singular ghost propagator and an almost linearly rising confinement potential. Using these solutions we calculate the electric field of static color charge distributions relevant for mesons and baryons.Comment: 4 pages, 5 figures, Proceedings ``Confinement Conference Sardinia 2004'

On the Yang-Mills wave functional in Coulomb gauge

We investigate the dependence of the Yang-Mills wave functional in Coulomb gauge on the Faddeev-Popov determinant. We use a Gaussian wave functional multiplied by an arbitrary power of the Faddeev-Popov determinant. We show, that within the resummation of one-loop diagrams the stationary vacuum energy is independent of the power of the Faddeev-Popov determinant and, furthermore, the wave functional becomes field-independent in the infrared, describing a stochastic vacuum. Our investigations show, that the infrared limit is rather robust against details of the variational ans\"atze for the Yang-Mills wave functional. The infrared limit is exclusively determined by the divergence of the Faddeev-Popov determinant at the Gribov horizon.Comment: 9 pages, no figure

The Yang-Mills Vacuum in Coulomb Gauge in D=2+1 Dimensions

The variational approach to the Hamilton formulation of Yang-Mills theory in Coulomb gauge developed by the present authors previously is applied to Yang-Mills theory in 2+1 dimensions and is confronted with the existing lattice data. We show that the resulting Dyson-Schwinger equations (DSE) yield consistent solutions in 2+1 dimensions only for infrared divergent ghost form factor and gluon energy. The obtained numerical solutions of the DSE reproduce the analytic infrared results and are in satisfactory agreement with the existing lattice date in the whole momentum range.Comment: 20 pages, 6 figure

Positive Effekte sozialen Faulenzens beim Lösen komplexer Probleme

Mit dem Begriff „Soziales Faulenzen“ sind Motivations- und Leistungsverluste in Gruppen bezeichnet worden, die durch sinkende Verantwortlichkeit der Gruppenteilnehmer für das Leistungsergebnis entstehen. Neuere Studien ließen daran Zweifel aufkommen und postulierten ein paradoxes Verhältnis von Motivation und Gruppenleistung derart, dass bei geringerer Motivation höhere Leistung zu erwarten sei. Die vorliegende Arbeit dient der Klärung dieser Frage. Es werden zwei Experimente berichtet, in denen jeweils 60 Personen in Dreiergruppen ein schwieriges computersimuliertes Waldbrand-Szenario (Networked Fire Chief) berarbeiteten. Variiert wurden die Schwierigkeit (leichte versus schwierigere Version) sowie die Verantwortlichkeit (koaktiv versus kollektiv). Während in Exp. 1 die Teilnehmenden nur auf dem ihnen zugewiesenen Spielfeld-Teil agieren konnten, konnten sie in Exp. 2 auf allen Teilfeldern agieren. Gemessen wurden Anstrengung und Leistung auf individueller wie Gruppenebene. Im Ergebnis zeigt sich unter Bedingungen kollektiver Verantwortlichkeit erwartungsgemäss ein Nachlassen der Anstrengung. Interessanterweise führt dies jedoch nicht zu einem Abfall der Leistung; unter der schwierigeren Bedingung zeigt sich sogar paradoxerweise eine erhöhte Leistung bei sinkender Anstrengung. Diskutiert werden die Konsequenzen für die Theorie kollektiver Anstrengung von Karau und Williams, deren Modell wohl um weitere Einflussfaktoren ergänzt werden muss

Complex Master Slave Interferometry

A general theoretical model is developed to improve the novel Spectral Domain Interferometry method denoted as Master/Slave (MS) Interferometry. In this model, two functions, g and h are introduced to describe the modulation chirp of the channeled spectrum signal due to nonlinearities in the decoding process from wavenumber to time and due to dispersion in the interferometer. The utilization of these two functions brings two major improvements to previous implementations of the MS method. A first improvement consists in reducing the number of channeled spectra necessary to be collected at Master stage. In previous MSI implementation, the number of channeled spectra at the Master stage equated the number of depths where information was selected from at the Slave stage. The paper demonstrates that two experimental channeled spectra only acquired at Master stage suffice to produce A-scans from any number of resolved depths at the Slave stage. A second improvement is the utilization of complex signal processing. Previous MSI implementations discarded the phase. Complex processing of the electrical signal determined by the channeled spectrum allows phase processing that opens several novel avenues. A first consequence of such signal processing is reduction in the random component of the phase without affecting the axial resolution. In previous MSI implementations, phase instabilities were reduced by an average over the wavenumber that led to reduction in the axial resolution

High precision planar waveguide propagation loss measurement technique using a Fabry-Perot cavity

A high precision measurement technique for characterizing the propagation loss in silica low-loss optical waveguides, based on measuring the contrast of a Fabry-Perot cavity, is demonstrated. The cavity consists of the waveguide coupled to two polarization-maintaining fibers, each end facet coated with dielectric mirrors, leaving the reflectivity as an adjustable parameter. The contrast is measured by modulating the cavity length without influence on the waveguide characteristics and the coupling efficiency. A double modulation of the cavity length reduces the measurement uncertainty, and provides a measurement precision better than 0.1 dB, corresponding to 0.02 dB/cm in case of a 5 cm long waveguid

Bridging the gap between geometric and algebraic multi-grid methods

In this paper, a multi-grid solver for the discretisation of partial differential equations on complicated domains is developed. The algorithm requires as input the given discretisation only instead of a hierarchy of discretisations on coarser grids. Such auxiliary grids and discretisations are generated in a black-box fashion and are employed to define purely algebraic intergrid transfer operators. The geometric interpretation of the algorithm allows one to use the framework of geometric multigrid methods to prove its convergence. The focus of this paper is on the formulation of the algorithm and the demonstration of its efficiency by numerical experiments, while the analysis is carried out for some model problems