A conjecture on Exceptional Orthogonal Polynomials

Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal polynomials. We formulate the following conjecture: every exceptional orthogonal polynomial system is related to a classical system by a Darboux-Crum transformation. We give a proof of this conjecture for codimension 2 exceptional orthogonal polynomials (X2-OPs). As a by-product of this analysis, we prove a Bochner-type theorem classifying all possible X2-OPS. The classification includes all cases known to date plus some new examples of X2-Laguerre and X2-Jacobi polynomials

Combined Effects of the North Atlantic Oscillation and the Arctic Oscillation on Sea Surface Temperature in the Alborán Sea

We explored the possible effects of the North Atlantic Oscillation (NAO) and Arctic Oscillation (AO) on interannual sea surface temperature (SST) variations in the Albora´n Sea, both separately and combined. The probability of observing mean annual SST values higher than average was related to NAO and AO values of the previous year. The effect of NAO on SST was negative, while that of AO was positive. The pure effects of NAO and AO on SST are obscuring each other, due to the positive correlation between them. When decomposing SST, NAO and AO in seasonal values, we found that variation in mean annual SST and mean winter SST was significantly related to the mean autumn NAO of the previous year, while mean summer SST was related to mean autumn AO of the previous year. The one year delay in the effect of the NAO and AO on the SST could be partially related to the amount of accumulated snow, as we found a significant correlation between the total snow in the North Albora´n watershed for a year with the annual average SST of the subsequent year. A positive AO implies a colder atmosphere in the Polar Regions, which could favour occasional cold waves over the Iberian Peninsula which, when coupled with precipitations favoured by a negative NAO, may result in snow precipitation. This snow may be accumulated in the high peaks and melt down in spring-summer of the following year, which consequently increases the runoff of freshwater to the sea, which in turn causes a diminution of sea surface salinity and density, and blocks the local upwelling of colder water, resulting in a higher SST.CGL2009-11316 (Ministerio de Ciencia e Innovación, Spain, and FEDER

Spin-phonon induced magnetic order in Kagome ice

We study the effects of lattice deformations on the Kagome spin ice, with Ising spins coupled by nearest neighbor exchange and long range dipolar interactions, in the presence of in-plane magnetic fields. We describe the lattice energy according to the Einstein model, where each site distortion is treated independently. Upon integration of lattice degrees of freedom, effective quadratic spin interactions arise. Classical MonteCarlo simulations are performed on the resulting model, retaining up to third neighbor interactions, under different directions of the magnetic field. We find that, as the effect of the deformation is increased, a rich plateau structure appears in the magnetization curves.Comment: 7 pages, 8 figure

Extragalactic Source Counts and Contributions to the Anisotropies of the Cosmic Microwave Background. Predictions for the Planck Surveyor mission

We present predictions for the counts of extragalactic sources, the contributions to fluctuations and their spatial power spectrum in each channel foreseen for the Planck Surveyor (formerly COBRAS/SAMBA) mission. The contribution to fluctuations due to clustering of both radio and far--IR sources is found to be generally small in comparison with the Poisson term; however the relative importance of the clustering contribution increases and may eventually become dominant if sources are identified and subtracted down to faint flux limits. The central Planck frequency bands are expected to be ``clean'': at high galactic latitude (|b|>20), where the reduced galactic noise does not prevent the detection of the extragalactic signal, only a tiny fraction of pixels is found to be contaminated by discrete extragalactic sources. Moreover, removal of contaminating signals is eased by the substantial difference between their power spectrum and that of primordial fluctuations.Comment: 10 pages, Latex, mn.sty, 8 figures included, MNRAS, in the press. Minor changes in the text. Sections 3.1 and 3.2 have been expanded. Source counts in Table 2 have been slightly changed. Figure 1,2,7 and 8 have been replaced by new version

Strong lensing by fermionic dark matter in galaxies

It has been shown that a self-gravitating system of massive keV fermions in thermodynamic equilibrium correctly describes the dark matter (DM) distribution in galactic halos and predicts a denser quantum core towards the center of the configuration. Such a quantum core, for a fermion mass in the range of $50$ keV $\lesssim m c^2 \lesssim 345$ keV, can be an alternative interpretation of the central compact object in Sgr A*. We present in this work the gravitational lensing properties of this novel DM model in Milky Way-like spiral galaxies. We describe the lensing effects of the pure DM component both on halo scales, where we compare them to the effects of the Navarro-Frenk-White and the Non-Singular Isothermal Sphere DM models, and near the galaxy center, where we compare them with the effects of a Schwarzschild BH. For the particle mass leading to the most compact DM core, $m c^2\approx 10^{2}$ keV, we draw the following conclusions. At distances $r\gtrsim 20$ pc from the center of the lens the effect of the central object on the lensing properties is negligible. However, we show that measurements of the deflection angle produced by the DM distribution in the outer region at a few kpc, together with rotation curve data, could help to discriminate between different DM models. We show that at distances $\sim 10^{-4}$ pc strong lensing effects, such as multiple images and Einstein rings, may occur. Large differences in the deflection angle produced by a DM central core and a central BH appear at distances $r\lesssim 10^{-6}$ pc; in this regime the weak-field formalism is no longer applicable and the exact general-relativistic formula has to be used. We find that quantum DM cores do not show a photon sphere what implies that they do not cast a shadow. Similar conclusions apply to the other DM distributions for other fermion masses in the above specified range and for other galaxy types.Comment: 10 pages, 8 figures. v2: Version published in PR

An Expanding HI Photodissociated Region Associated with the Compact HII Region G213.880-11.837 in the GGD 14 Complex

We present high angular and spectral resolution HI 21~cm line observations toward the cometary-shaped compact HII region G213.880-11.837 in the GGD~14 complex.The kinematics and morphology of the photodissociated region, traced by the HI line emission, reveal that the neutral gas is part of an expanding flow. The kinematics of the HI gas along the major axis of G213.880-11.837 shows that the emission is very extended toward the SE direction, reaching LSR radial velocities in the tail of about 14 km/s. The ambient LSR radial velocity of the molecular gas is 11.5 km/s, which suggests a champagne flow of the HI gas. This is the second (after G111.61+0.37) cometary HII/HI region known.Comment: Accepted for publication in the Astronomical Journal (10 pages, 4 figures, 1 table

Coherent coupling between surface plasmons and excitons in semiconductor nanocrystals

We present an experimental demonstration of strong coupling between a surface plasmon propagating on a planar silver substrate, and the lowest excited state of CdSe nanocrystals. Variable-angle spectroscopic ellipsometry measurements demonstrated the formation of plasmon-exciton mixed states, characterized by a Rabi splitting of $\sim$ 82 meV at room temperature. Such a coherent interaction has the potential for the development of plasmonic non-linear devices, and furthermore, this system is akin to those studied in cavity quantum electrodynamics, thus offering the possibility to study the regime of strong light-matter coupling in semiconductor nanocrystals at easily accessible experimental conditions.Comment: 12 pages, 4 figure