About the Power to Enforce and Prevent Consensus by Manipulating Communication Rules

We explore the possibilities of enforcing and preventing consensus in continuous opinion dynamics that result from modifications in the communication rules. We refer to the model of Weisbuch and Deffuant, where $n$ agents adjust their continuous opinions as a result of random pairwise encounters whenever their opinions differ not more than a given bound of confidence \eps. A high \eps leads to consensus, while a lower \eps leads to a fragmentation into several opinion clusters. We drop the random encounter assumption and ask: How small may \eps be such that consensus is still possible with a certain communication plan for the entire group? Mathematical analysis shows that \eps may be significantly smaller than in the random pairwise case. On the other hand we ask: How large may \eps be such that preventing consensus is still possible? In answering this question we prove Fortunato's simulation result that consensus cannot be prevented for \eps>0.5 for large groups. % Next we consider opinion dynamics under different individual strategies and examine their power to increase the chances of consensus. One result is that balancing agents increase chances of consensus, especially if the agents are cautious in adapting their opinions. However, curious agents increase chances of consensus only if those agents are not cautious in adapting their opinions.Comment: 21 pages, 6 figure

Modified Lattice Landau Gauge

We propose a modified lattice Landau gauge based on stereographically projecting the link variables on the circle S^1 -> R for compact U(1) or the 3-sphere S^3 -> R^3 for SU(2) before imposing the Landau gauge condition. This can reduce the number of Gribov copies exponentially and solves the Gribov problem in compact U(1) where it is a lattice artifact. Applied to the maximal Abelian subgroup this might be just enough to avoid the perfect cancellation amongst the Gribov copies in a lattice BRST formulation for SU(N), and thus to avoid the Neuberger 0/0 problem. The continuum limit of the Landau gauge remains unchanged.Comment: 7 pages, 2 figures, for the proceedings of the XXV International Symposium on Lattice Field Theory, July 30 - August 4 2007, Regensburg, German

Influence of the quantum zero-point motion of a vortex on the electronic spectra of s-wave superconductors

We compute the influence of the quantum zero-point motion of a vortex on the electronic quasiparticle spectra of s-wave superconductors. The vortex is assumed to be pinned by a harmonic potential, and its coupling to the quasiparticles is computed in the framework of BCS theory. Near the core of the vortex, the motion leads to a shift of spectral weight away from the chemical potential, and thereby reduces the zero bias conductance peak; additional structure at the frequency of the harmonic trap is also observed.Comment: 14 pages, 7 figures; (v2) added refs; (v3) removed discussion on d-wave superconductors and moved it to cond-mat/060600

Bound states of negatively charged ions induced by a magnetic field

We analyse the bound states of negatively charged ions which were predicted to exist because of the presence of a magnetic field by Avron et al. We confirm that the number of such states is infinite in the approximation of an infinitely heavy nucleus and provide insight into the underlying physical picture by means of a combined adiabatic and perturbation theoretical approach. We also calculate the corresponding binding energies which are qualitatively different for the states with vanishing and non-vanishing angular momentum. An outlook on the case of including center of mass effects is presented.Comment: 14 pages, 2 figure

A simple closure approximation for slow dynamics of a multiscale system: nonlinear and multiplicative coupling

Multiscale dynamics are ubiquitous in applications of modern science. Because of time scale separation between relatively small set of slowly evolving variables and (typically) much larger set of rapidly changing variables, direct numerical simulations of such systems often require relatively small time discretization step to resolve fast dynamics, which, in turn, increases computational expense. As a result, it became a popular approach in applications to develop a closed approximate model for slow variables alone, which both effectively reduces the dimension of the phase space of dynamics, as well as allows for a longer time discretization step. In this work we develop a new method for approximate reduced model, based on the linear fluctuation-dissipation theorem applied to statistical states of the fast variables. The method is suitable for situations with quadratically nonlinear and multiplicative coupling. We show that, with complex quadratically nonlinear and multiplicative coupling in both slow and fast variables, this method produces comparable statistics to what is exhibited by an original multiscale model. In contrast, it is observed that the results from the simplified closed model with a constant coupling term parameterization are consistently less precise

Abnormal Rolls and Regular Arrays of Disclinations in Homeotropic Electroconvection

We present the first quantitative verification of an amplitude description for systems with (nearly) spontaneously broken isotropy, in particular for the recently discovered abnormal-roll states. We also obtain a conclusive picture of the 3d director configuration in a spatial period doubling phenomenon involving disclination loops (CRAZY rolls). The first observation of two Lifshitz frequencies in electroconvection is reported.Comment: 4 pages; 4 figure

New structures in the proton-antiproton system

In the most recent measurements of the reaction $e^+e^- \rightarrow p\bar{p}$ by the BABAR collaboration, new structures have been found with unknown origin. We examine a possible relation of the most distinct peak to the recently observed $\Phi(2170)$. Alternatively, we analyse possible explanations due to the nucleon$\,\bar{\Delta}$ and $\Delta\bar{\Delta}$ thresholds. The latter could explain a periodicity found in the data