Making electromagnetic wavelets

Electromagnetic wavelets are constructed using scalar wavelets as superpotentials, together with an appropriate polarization. It is shown that oblate spheroidal antennas, which are ideal for their production and reception, can be made by deforming and merging two branch cuts. This determines a unique field on the interior of the spheroid which gives the boundary conditions for the surface charge-current density necessary to radiate the wavelets. These sources are computed, including the impulse response of the antenna.Comment: 29 pages, 4 figures; minor corrections and addition

Shielding and localization in presence of long range hopping

We investigate a paradigmatic model for quantum transport with both nearest-neighbor and infinite range hopping coupling (independent of the position). Due to long range homogeneous hopping, a gap between the ground state and the excited states can be induced, which is mathematically equivalent to the superconducting gap. In the gapped regime, the dynamics within the excited states subspace is shielded from long range hopping, namely it occurs as if long range hopping would be absent. This is a cooperative phenomenon since shielding is effective over a time scale which diverges with the system size. We named this effect {\it Cooperative Shielding}. We also discuss the consequences of our findings on Anderson localization. Long range hopping is usually thought to destroy localization due to the fact that it induces an infinite number of resonances. Contrary to this common lore we show that the excited states display strong localized features when shielding is effective even in the regime of strong long range coupling. A brief discussion on the extension of our results to generic power-law decaying long range hopping is also given. Our preliminary results confirms that the effects found for the infinite range case are generic.Comment: 7 pages, 9 figur

Novel approach to pion and eta production in proton-proton collisions near threshold

We evaluate the threshold matrix-element for the reaction $pp \to pp\pi^0$ in a fully relativistic Feynman diagrammatic approach. We employ a simple effective range approximation to take care of the S-wave $pp$ final-state interaction. The experimental value for the threshold amplitude ${\cal A} = (2.7 - i 0.3)$ fm$^4$ can be reproduced by contributions from tree level chiral (long-range) pion exchange and short-range effects related to vector meson exchanges, with $\omega$ exchange giving the largest individual contribution. Pion loop effects appear to be small. We stress that the commonly used heavy baryon formalism is not applicable in the NN-system above the pion production threshold due to the large external momentum, $|\vec p | \simeq \sqrt {Mm_\pi}$, with $M$ and $m_\pi$ the nucleon and the pion mass, respectively. We furthermore investigate the reaction $pp\to p n \pi^+$ near threshold within the same approach. We extract from the data the triplet threshold amplitude as ${\cal B}= (2.8 -i 1.5)$ fm$^4$. Its real part can be well understood from (relativistic) tree level meson-exchange diagrams. In addition, we investigate the process $pp \to pp \eta$ near threshold. We use a simple factorization ansatz for the $pp\eta$ final-state interaction and extract from the data the modulus of the threshold amplitude, $|{\cal C}| = 1.32$fm$^4$. With $g_{\eta N}=5.3$, this value can be reproduced by (relativistic) tree level meson-exchange diagrams and $\eta$-rescattering, whose strength is fixed by the $\eta N$ scattering length. We also comment on the recent near threshold data for $\eta'$-production.Comment: 28 pp, LaTeX, 9 figs, uses epsf, updated version. To be published in Eur. Phys. J. A (1999). **Title changed again*

The fractional chromatic number of triangle-free subcubic graphs

Heckman and Thomas conjectured that the fractional chromatic number of any triangle-free subcubic graph is at most 14/5. Improving on estimates of Hatami and Zhu and of Lu and Peng, we prove that the fractional chromatic number of any triangle-free subcubic graph is at most 32/11 (which is roughly 2.909)

A Weak Gravitational Lensing Analysis of Abell 2390

We report on the detection of dark matter in the cluster Abell 2390 using the weak gravitational distortion of background galaxies. We find that the cluster light and total mass distributions are quite similar over an angular scale of \simeq 7^\prime \;(1 \Mpc). The cluster galaxy and mass distributions are centered on the cluster cD galaxy and exhibit elliptical isocontours in the central \simeq 2^\prime \; (280 \kpc). The major axis of the ellipticity is aligned with the direction defined by the cluster cD and a ``straight arc'' located $\simeq 38^{\prime\prime}$ to the northwest. We determined the radial mass-to-light profile for this cluster and found a constant value of $(320 \pm 90) h\; M_\odot/L_{\odot V}$, which is consistent with other published determinations. We also compared our weak lensing azimuthally averaged radial mass profile with a spherical mass model proposed by the CNOC group on the basis of their detailed dynamical study of the cluster. We find good agreement between the two profiles, although there are weak indications that the CNOC density profile may be falling more steeply for $\theta\geq 3^\prime$ (420\kpc).Comment: 14 pages, latex file. Postscript file and one additional figure are available at ftp://magicbean.berkeley.edu/pub/squires/a2390/massandlight.ps.g