Geometric phases in 2D and 3D polarized fields: geometrical, dynamical, and topological aspects

Geometric phases are a universal concept that underpins numerous phenomena involving multi-component wave fields. These polarization-dependent phases are inherent in interference effects, spin-orbit interaction phenomena, and topological properties of vector wave fields. Geometric phases have been thoroughly studied in two-component fields, such as two-level quantum systems or paraxial optical waves. However, their description for fields with three or more components, such as generic nonparaxial optical fields routinely used in modern nano-optics, constitutes a nontrivial problem. Here we describe geometric, dynamical, and total phases calculated along a closed spatial contour in a multi-component complex field, with particular emphasis on 2D (paraxial) and 3D (nonparaxial) optical fields. We present several equivalent approaches: (i) an algebraic formalism, universal for any multi-component field; (ii) a dynamical approach using the Coriolis coupling between the spin angular momentum and reference-frame rotations; and (iii) a geometric representation, which unifies the Pancharatnam-Berry phase for the 2D polarization on the Poincar\'e sphere and the Majorana-sphere representation for the 3D polarized fields. Most importantly, we reveal close connections between geometric phases, angular-momentum properties of the field, and topological properties of polarization singularities in 2D and 3D fields, such as C-points and polarization M\"obius strips.Comment: 21 pages, 11 figures, to appear in Rep. Prog. Phy

Order N Monte Carlo Algorithm for Fermion Systems Coupled with Fluctuating Adiabatical Fields

An improved algorithm is proposed for Monte Carlo methods to study fermion systems interacting with adiabatical fields. To obtain a weight for each Monte Carlo sample with a fixed configuration of adiabatical fields, a series expansion using Chebyshev polynomials is applied. By introducing truncations of matrix operations in a systematic and controlled way, it is shown that the cpu time is reduced from O(N^3) to O(N) where N is the system size. Benchmark results show that the implementation of the algorithm makes it possible to perform systematic investigations of critical phenomena using system-size scalings even for an electronic model in three dimensions, within a realistic cpu timescale.Comment: 9 pages with 4 fig

Angular Momenta and Spin-Orbit Interaction of Nonparaxial Light in Free Space

We give an exact self-consistent operator description of the spin and orbital angular momenta, position, and spin-orbit interactions of nonparaxial light in free space. Both quantum-operator formalism and classical energy-flow approach are presented. We apply the general theory to symmetric and asymmetric Bessel beams exhibiting spin- and orbital-dependent intensity profiles. The exact wave solutions are clearly interpreted in terms of the Berry phases, quantization of caustics, and Hall effects of light, which can be readily observed experimentally.Comment: 8 pages, 3 figure

On the Complexity of Solving Zero-Dimensional Polynomial Systems via Projection

Given a zero-dimensional polynomial system consisting of n integer polynomials in n variables, we propose a certified and complete method to compute all complex solutions of the system as well as a corresponding separating linear form l with coefficients of small bit size. For computing l, we need to project the solutions into one dimension along O(n) distinct directions but no further algebraic manipulations. The solutions are then directly reconstructed from the considered projections. The first step is deterministic, whereas the second step uses randomization, thus being Las-Vegas. The theoretical analysis of our approach shows that the overall cost for the two problems considered above is dominated by the cost of carrying out the projections. We also give bounds on the bit complexity of our algorithms that are exclusively stated in terms of the number of variables, the total degree and the bitsize of the input polynomials

Universality Class of Ferromagnetic Transition in Three-Dimensional Double-Exchange System - O(N) Monte Carlo Study -

Curie temperature and exponents are studied for the three-dimensional double-exchange model. Applying the O(N) Monte Carlo algorithm, we perform systematic finite-size scaling analyses on the data up to $20^3$ sites. The obtained values of the critical exponents are consistent with those of the Heisenberg universality class, and clearly distinct from the mean-field values.Comment: 3 pages including 2 figure

Cooler and bigger than thought? Planetary host stellar parameters from the InfraRed Flux Method

Effective temperatures and radii for 92 planet-hosting stars as determined from the InfraRed Flux Method (IRFM) are presented and compared with those given by other authors using different approaches. The IRFM temperatures we have derived are systematically lower than those determined from the spectroscopic condition of excitation equilibrium, the mean difference being as large as 110 K. They are, however, consistent with previous IRFM studies and with the colors derived from Kurucz and MARCS model atmospheres. Comparison with direct measurements of stellar diameters for 7 dwarf stars, which approximately cover the range of temperatures of the planet-hosting stars, suggest that the IRFM radii and temperatures are reliable in an absolute scale. A better understanding of the fundamental properties of the stars with planets will be achieved once this discrepancy between the IRFM and the spectroscopic temperature scales is resolved.Comment: 15 pages, 4 figures. Accepted for publication in Ap

Past alcohol consumption and incident atrial fibrillation: The Atherosclerosis Risk in Communities (ARIC) Study.

BackgroundAlthough current alcohol consumption is a risk factor for incident atrial fibrillation (AF), the more clinically relevant question may be whether alcohol cessation is associated with a reduced risk.Methods and resultsWe studied participants enrolled in the Atherosclerosis Risk in Communities Study (ARIC) between 1987 and 1989 without prevalent AF. Past and current alcohol consumption were ascertained at baseline and at 3 subsequent visits. Incident AF was ascertained via study ECGs, hospital discharge ICD-9 codes, and death certificates. Of 15,222 participants, 2,886 (19.0%) were former drinkers. During a median follow-up of 19.7 years, there were 1,631 cases of incident AF, 370 occurring in former consumers. Former drinkers had a higher rate of AF compared to lifetime abstainers and current drinkers. After adjustment for potential confounders, every decade abstinent from alcohol was associated with an approximate 20% (95% CI 11-28%) lower rate of incident AF; every additional decade of past alcohol consumption was associated with a 13% (95% CI 3-25%) higher rate of AF; and every additional drink per day during former drinking was associated with a 4% (95% CI 0-8%) higher rate of AF.ConclusionsAmong former drinkers, the number of years of drinking and the amount of alcohol consumed may each confer an increased risk of AF. Given that a longer duration of abstinence was associated with a decreased risk of AF, earlier modification of alcohol use may have a greater influence on AF prevention

Algunos Euménidos y Masáridos del Norte de Africa (Hym. Vesp.)

El distinguido himenopterólogo M. Paúl Th. Roth, de Argel, que reune Esfégidos de Argelia, y ha publicado sobre ellos notables trabajos, me envió un interesante lote de Véspidos, entre los que hay varias novedades. A la vez pude estudiar algunos que me ha remitido el Barón Francesco Biegeleben, de Appiano (Italia), fruto de una excursión de su primo, Barón Pietro Giovanelli. También los he recibido del Dr. Santschi, de Kairouan (Túnez), y he revisado varios, de distintas procedencias, que tenía en mi colección, y unos pocos ingresados en el Museo de Madrid con posterioridad a mi trabajo sobre los de Marruecos. (Memorias R. Soc. Esp. H. Natural, t. VIII. Mem. 9ª Madrid, 1917).Peer reviewe

Dos Odynerus y un Gorytes nuevos de Marruecos con una lista de ápidos (Hymenopt.)

En la última visita hecha a este Museo por el distinguido entomólogo y viajero francés M. Charles Alluaud, tuve ocasión de ver algunas especies de himenópteros, cazadas por él, que describo o menciono a continuación.Peer reviewe

Nuevas prácticas de "Dry-Farming" en España : conferencia leída en la "Semana agrícola" de Valladolid

Precede al tít.: Asociación de Agricultores de EspañaCopia digital. Valladolid : Junta de Castilla y León. Consejería de Cultura y Turismo, 201