Quantized Non-Abelian Monopoles on S^3

A possible electric-magnetic duality suggests that the confinement of non-Abelian electric charges manifests itself as a perturbative quantum effect for the dual magnetic charges. Motivated by this possibility, we study vacuum fluctuations around a non-Abelian monopole-antimonopole pair treated as point objects with charges g=\pm n/2 (n=1,2,...), and placed on the antipodes of a three sphere of radius R. We explicitly find all the fluctuation modes by linearizing and solving the Yang-Mills equations about this background field on a three sphere. We recover, generalize and extend earlier results, including those on the stability analysis of non-Abelian magnetic monopoles. We find that for g \ge 1 monopoles there is an unstable mode that tends to squeeze magnetic flux in the angular directions. We sum the vacuum energy contributions of the fluctuation modes for the g=1/2 case and find oscillatory dependence on the cutoff scale. Subject to certain assumptions, we find that the contribution of the fluctuation modes to the quantum zero point energy behaves as -R^{-2/3} and hence decays more slowly than the classical -R^{-1} Coulomb potential for large R. However, this correction to the zero point energy does not agree with the linear growth expected if the monopoles are confined.Comment: 18 pages, 5 figures. Minor changes, reference list update

Giant Magnetic Moments of Nitrogen Stabilized Mn Clusters and Their Relevance to Ferromagnetism in Mn Doped GaN

Using first principles calculations based on density functional theory, we show that the stability and magnetic properties of small Mn clusters can be fundamentally altered by the presence of nitrogen. Not only are their binding energies substantially enhanced, but also the coupling between the magnetic moments at Mn sites remains ferromagnetic irrespective of their size or shape. In addition, these nitrogen stabilized Mn clusters carry giant magnetic moments ranging from 4 Bohr magnetons in MnN to 22 Bohr magnetons in Mn_5N. It is suggested that the giant magnetic moments of Mn_xN clusters may play a key role in the ferromagnetism of Mn doped GaN which exhibit a wide range (10K - 940K) of Curie temperatures

Power counting with one-pion exchange

Techniques developed for handing inverse-power-law potentials in atomic physics are applied to the tensor one-pion exchange potential to determine the regions in which it can be treated perturbatively. In S-, P- and D-waves the critical values of the relative momentum are less than or of the order of 400 MeV. The RG is then used to determine the power counting for short-range interaction in the presence of this potential. In the P-and D-waves, where there are no low-energy bound or virtual states, these interactions have half-integer RG eigenvalues and are substantially promoted relative to naive expectations. These results are independent of whether the tensor force is attractive or repulsive. In the 3S1 channel the leading term is relevant, but it is demoted by half an order compared to the counting for the effective-range expansion with only a short-range potential. The tensor force can be treated perturbatively in those F-waves and above that do not couple to P- or D-waves. The corresponding power counting is the usual one given by naive dimensional analysis.Comment: 18 pages, RevTeX (further details, explanation added

Removal of terrestrial DOC in aquatic ecosystems of a temperate river network

Surface waters play a potentially important role in the global carbon balance. Dissolved organic carbon (DOC) fluxes are a major transfer of terrestrial carbon to river systems, and the fate of DOC in aquatic systems is poorly constrained. We used a unique combination of spatially distributed sampling of three DOC fractions throughout a river network and modeling to quantify the net removal of terrestrial DOC during a summer base flow period. We found that aquatic reactivity of terrestrial DOC leading to net loss is low, closer to conservative chloride than to reactive nitrogen. Net removal occurred mainly from the hydrophobic organic acid fraction, while hydrophilic and transphilic acids showed no net change, indicating that partitioning of bulk DOC into different fractions is critical for understanding terrestrial DOC removal. These findings suggest that river systems may have only a modest ability to alter the amounts of terrestrial DOC delivered to coastal zones

Circular dielectric cavity and its deformations

The construction of perturbation series for slightly deformed dielectric circular cavity is discussed in details. The obtained formulae are checked on the example of cut disks. A good agreement is found with direct numerical simulations and far-field experiments.Comment: 17 pages, 12 figure

On separable Fokker-Planck equations with a constant diagonal diffusion matrix

We classify (1+3)-dimensional Fokker-Planck equations with a constant diagonal diffusion matrix that are solvable by the method of separation of variables. As a result, we get possible forms of the drift coefficients $B_1(\vec x),B_2(\vec x),B_3(\vec x)$ providing separability of the corresponding Fokker-Planck equations and carry out variable separation in the latter. It is established, in particular, that the necessary condition for the Fokker-Planck equation to be separable is that the drift coefficients $\vec B(\vec x)$ must be linear. We also find the necessary condition for R-separability of the Fokker-Planck equation. Furthermore, exact solutions of the Fokker-Planck equation with separated variables are constructedComment: 20 pages, LaTe

Those wonderful elastic waves

We consider in a simple and general way elastic waves in isotropic and anisotropic media, their polarization, speeds, reflection from interfaces with mode conversion, and surface waves. Reflection of quasi transverse waves in anisotropic media from a free surface is shown to be characterized by three critical angles.Comment: 11 Figures 26 page

Bound-States of the Spinless Salpeter Equation for the PT-Symmetric Generalized Hulthen Potential by the Nikiforov-Uvarov Method

The one-dimensional spinless Salpeter equation has been solved for the PT-symmetric generalized Hulth\'{e}n potential. The Nikiforov-Uvarov {NU) method which is based on solving the second-order linear differential equations by reduction to a generalized equation of hypergeometric type is used to obtain exact energy eigenvalues and corresponding eigenfunctions. We have investigated the positive and negative exact bound states of the s-states for different types of complex generalized Hulthen potentials.Comment: 24 page

Waiting in the Wings: Reflected X-ray Emission from the Homunculus Nebula

We report the first detection of X-ray emission associated with the Homunculus Nebula which surrounds the supermassive star Eta Carinae. The emission is characterized by a temperature in excess of 100 MK, and is consistent with scattering of the time-delayed X-ray flux associated with the star. The nebular emission is bright in the northwestern lobe and near the central regions of the Homunculus, and fainter in the southeastern lobe. We also report the detection of an unusually broad Fe K fluorescent line, which may indicate fluorescent scattering off the wind of a companion star or some other high velocity outflow. The X-ray Homunculus is the nearest member of the small class of Galactic X-ray reflection nebulae, and the only one in which both the emitting and reflecting sources are distinguishable.Comment: 17 pages, 5 figures, accepted by Ap

Taylor dispersion with absorbing boundaries: A Stochastic Approach

We describe how to solve the problem of Taylor dispersion in the presence of absorbing boundaries using an exact stochastic formulation. In addition to providing a clear stochastic picture of Taylor dispersion, our method leads to closed-form expressions for all the moments of the convective displacement of the dispersing particles in terms of the transverse diffusion eigenmodes. We also find that the cumulants grow asymptotically linearly with time, ensuring a Gaussian distribution in the long-time limit. As a demonstration of the technique, the first two longitudinal cumulants (yielding respectively the effective velocity and the Taylor diffusion constant) as well as the skewness (a measure of the deviation from normality) are calculated for fluid flow in the parallel plate geometry. We find that the effective velocity and the skewness (which is negative in this case) are enhanced while Taylor dispersion is suppressed due to absorption at the boundary.Comment: 4 pages, 1 figur