Christoffel functions and orthogonal polynomials for Erd¨os weights on (–∞,∞)

We establish bounds on orthonormal polynomials and Christoffel functions associated with weights on IR of the form W2 = e−2Q, where Q : IR → IR is even, and is of faster than polynomial growth at ∞ (so-called Erd¨os weights). Typical examples are Q(x) := expk |x| α1, α > 1, , where expk = expk (exp (... exp(·))) denotes the kth iterated exponential. Further, we obtain uniform estimates on the spacing of all the zeros and on the Christoffel functions. These results complement earlier ones for the case where Q is of polynomial growth at ∞ (so-called Freud weights) and for exponential weights on (−1, 1)

The Landshoff-Nachtmann Pomeron on the Lattice

We investigate the Landshoff-Nachtmann two-gluon-exchange model of the Pomeron using gluon propagators computed in the Landau gauge within quenched lattice QCD calculations. We first determine an effective gluon-quark coupling by constraining the Pomeron-quark coupling to its phenomenological value \beta_0 = 2\, \gev^{-1}. We then provide predictions for a variety of diffractive processes. As the propagators have been evaluated entirely from QCD first principles (although in the quenched approximation), our results provide a consistency check of the Landshoff-Nachtmann model. We address the issue of the possible gauge-dependence of our results, which will be the object of a future study.Comment: uuencoded, compressed tar file, 13 pages latex, 4 Postscript figures, requires epsf.st

Nanoscale polar heterogeneities and branching Bi-displacement directions in K0.5Bi0.5TiO3

K0.5Bi0.5TiO3 (KBT)—one of the few perovskite-like ferroelectric compounds with room-temperature tetragonal symmetry—differs from other members of its family (BaTiO3 and PbTiO3) by the presence of a disordered mixture of K and Bi on cuboctahedral sites. This disorder is expected to affect local atomic displacements and their response to an applied electric field. We have derived nanoscale atomistic models of KBT by refining atomic coordinates to simultaneously fit neutron/X-ray total scattering and extended X-ray absorption fine-structure data. Both Bi and Ti ions were found to be offset relative to their respective oxygen cages in the high-temperature cubic phase; in contrast, the coordination environment of K remained relatively undistorted. In the cubic structure, Bi displacements prefer the ⟨100⟩ directions and the probability density distribution of Bi features six well-separated sites; a similar preference exists for the much smaller Ti displacements, although the split sites for Ti could not be resolved. The cation displacements are correlated, yielding polar nanoregions, whereas on average, the structure appears as cubic. The cubic ↔ tetragonal phase transition involves both order/disorder and displacive mechanisms. A qualitative change in the form of the Bi probability density distribution occurs in the tetragonal phase on cooling to room temperature because Bi displacements “branch off” to ⟨111⟩ directions. This change, which preserves the average symmetry, is accompanied by the development of nanoscale polar heterogeneities that exhibit significant deviations of their polarization vectors from the average polar axis

Patchiness and Demographic Noise in Three Ecological Examples

Understanding the causes and effects of spatial aggregation is one of the most fundamental problems in ecology. Aggregation is an emergent phenomenon arising from the interactions between the individuals of the population, able to sense only -at most- local densities of their cohorts. Thus, taking into account the individual-level interactions and fluctuations is essential to reach a correct description of the population. Classic deterministic equations are suitable to describe some aspects of the population, but leave out features related to the stochasticity inherent to the discreteness of the individuals. Stochastic equations for the population do account for these fluctuation-generated effects by means of demographic noise terms but, owing to their complexity, they can be difficult (or, at times, impossible) to deal with. Even when they can be written in a simple form, they are still difficult to numerically integrate due to the presence of the "square-root" intrinsic noise. In this paper, we discuss a simple way to add the effect of demographic stochasticity to three classic, deterministic ecological examples where aggregation plays an important role. We study the resulting equations using a recently-introduced integration scheme especially devised to integrate numerically stochastic equations with demographic noise. Aimed at scrutinizing the ability of these stochastic examples to show aggregation, we find that the three systems not only show patchy configurations, but also undergo a phase transition belonging to the directed percolation universality class.Comment: 20 pages, 5 figures. To appear in J. Stat. Phy

Displacive order–disorder behavior and intrinsic clustering of lattice distortions in bi‐substituted NaNbO3

Perovskite‐like NaNbO3‐Bi1/3NbO3 solid solutions are studied to understand the interactions between octahedral rotations, which dominate the structural behavior of NaNbO3 and displacive disorder of Bi present in Bi1/3NbO3. Models of instantaneous structures for representative compositions are obtained by refining atomic coordinates against X‐ray total scattering and extended X‐ray‐absorption fine structure data, with additional input obtained from transmission electron microscopy. A mixture of distinct cations and vacancies on the cuboctahedral A‐sites in Na1−3x Bix NbO3 (x ≤ 0.2) results in 3D nanoscale modulations of structural distortions. This phenomenon is determined by the inevitable correlations in the chemical composition of adjacent unit cells according to the structure type—an intrinsic property of any nonmolecular crystals. Octahedral rotations become suppressed as x increases. Out‐of‐phase rotations vanish for x > 0.1, whereas in‐phase tilts persist up to x = 0.2, although for this composition their correlation length becomes limited to the nanoscale. The loss of out‐of‐phase tilting is accompanied by qualitative changes in the probability density distributions for Bi and Nb, with both species becoming disordered over loci offset from the centers of their respective oxygen cages. Symmetry arguments are used to attribute this effect to different strengths of the coupling between the cation displacements and out‐of‐phase versus in‐phase rotations. The displacive disorder of Bi and Nb combined with nanoscale clustering of lattice distortions are primarily responsible for the anomalous broadening of the temperature dependence of the dielectric constant

Streamlined Calibrations of the ATLAS Precision Muon Chambers for Initial LHC Running

The ATLAS Muon Spectrometer is designed to measure the momentum of muons with a resolution of dp/p = 3% and 10% at 100 GeV and 1 TeV momentum respectively. For this task, the spectrometer employs 355,000 Monitored Drift Tubes (MDTs) arrayed in 1200 Chambers. Calibration (RT) functions convert drift time measurements into tube-centered impact parameters for track segment reconstruction. RT functions depend on MDT environmental parameters and so must be appropriately calibrated for local chamber conditions. We report on the creation and application of a gas monitor system based calibration program for muon track reconstruction in the LHC startup phase.Comment: 25 pages, 21 figure

Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet

We study the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice in the limit of strong easy-axis exchange anisotropy. We find, using only standard techniques of degenerate perturbation theory, that the model has a U(1) gauge symmetry generated by certain local rotations about the z-axis in spin space. Upon addition of an extra local interaction in this and a related model with spins on a three-dimensional network of corner-sharing octahedra, we can write down the exact ground state wavefunction with no further approximations. Using the properties of the soluble point we show that these models enter the U(1) spin liquid phase, a novel fractionalized spin liquid with an emergent U(1) gauge structure. This phase supports gapped S^z = 1/2 spinons carrying the U(1) ``electric'' gauge charge, a gapped topological point defect or ``magnetic'' monopole, and a gapless ``photon,'' which in spin language is a gapless, linearly dispersing S^z = 0 collective mode. There are power-law spin correlations with a nontrivial angular dependence, as well as novel U(1) topological order. This state is stable to ALL zero-temperature perturbations and exists over a finite extent of the phase diagram. Using a convenient lattice version of electric-magnetic duality, we develop the effective description of the U(1) spin liquid and the adjacent soluble point in terms of Gaussian quantum electrodynamics and calculate a few of the universal properties. The resulting picture is confirmed by our numerical analysis of the soluble point wavefunction. Finally, we briefly discuss the prospects for understanding this physics in a wider range of models and for making contact with experiments.Comment: 22 pages, 14 figures. Further minor changes. To appear in Phys. Rev.

Electrical transport studies of quench condensed Bi films at the initial stage of film growth: Structural transition and the possible formation of electron droplets

The electrical transport properties of amorphous Bi films prepared by sequential quench deposition have been studied in situ. A superconductor-insulator (S-I) transition was observed as the film was made increasingly thicker, consistent with previous studies. Unexpected behavior was found at the initial stage of film growth, a regime not explored in detail prior to the present work. As the temperature was lowered, a positive temperature coefficient of resistance (dR/dT > 0) emerged, with the resistance reaching a minimum before the dR/dT became negative again. This behavior was accompanied by a non-linear and asymmetric I-V characteristic. As the film became thicker, conventional variable-range hopping (VRH) was recovered. We attribute the observed crossover in the electrical transport properties to an amorphous to granular structural transition. The positive dR/dT found in the amorphous phase of Bi formed at the initial stage of film growth was qualitatively explained by the formation of metallic droplets within the electron glass.Comment: 7 pages, 6 figure

Interactions, Distribution of Pinning Energies, and Transport in the Bose Glass Phase of Vortices in Superconductors

We study the ground state and low energy excitations of vortices pinned to columnar defects in superconductors, taking into account the long--range interaction between the fluxons. We consider the ``underfilled'' situation in the Bose glass phase, where each flux line is attached to one of the defects, while some pins remain unoccupied. By exploiting an analogy with disordered semiconductors, we calculate the spatial configurations in the ground state, as well as the distribution of pinning energies, using a zero--temperature Monte Carlo algorithm minimizing the total energy with respect to all possible one--vortex transfers. Intervortex repulsion leads to strong correlations whenever the London penetration depth exceeds the fluxon spacing. A pronounced peak appears in the static structure factor $S(q)$ for low filling fractions $f \leq 0.3$. Interactions lead to a broad Coulomb gap in the distribution of pinning energies $g(\epsilon)$ near the chemical potential $\mu$, separating the occupied and empty pins. The vanishing of $g(\epsilon)$ at $\mu$ leads to a considerable reduction of variable--range hopping vortex transport by correlated flux line pinning.Comment: 16 pages (twocolumn), revtex, 16 figures not appended, please contact [email protected]