On the rational subset problem for groups

We use language theory to study the rational subset problem for groups and monoids. We show that the decidability of this problem is preserved under graph of groups constructions with finite edge groups. In particular, it passes through free products amalgamated over finite subgroups and HNN extensions with finite associated subgroups. We provide a simple proof of a result of Grunschlag showing that the decidability of this problem is a virtual property. We prove further that the problem is decidable for a direct product of a group G with a monoid M if and only if membership is uniformly decidable for G-automata subsets of M. It follows that a direct product of a free group with any abelian group or commutative monoid has decidable rational subset membership.Comment: 19 page

Radiative corrections in bumblebee electrodynamics

We investigate some quantum features of the bumblebee electrodynamics in flat spacetimes. The bumblebee field is a vector field that leads to a spontaneous Lorentz symmetry breaking. For a smooth quadratic potential, the massless excitation (Nambu-Goldstone boson) can be identified as the photon, transversal to the vacuum expectation value of the bumblebee field. Besides, there is a massive excitation associated with the longitudinal mode and whose presence leads to instability in the spectrum of the theory. By using the principal-value prescription, we show that no one-loop radiative corrections to the mass term is generated. Moreover, the bumblebee self-energy is not transverse, showing that the propagation of the longitudinal mode can not be excluded from the effective theory.Comment: Revised version: contains some more elaborated interpretation of the results. Conclusions improve

Magnetic monopole and string excitations in a two-dimensional spin ice

We study the magnetic excitations of a square lattice spin-ice recently produced in an artificial form, as an array of nanoscale magnets. Our analysis, based upon the dipolar interaction between the nanomagnetic islands, correctly reproduces the ground-state observed experimentally. In addition, we find magnetic monopole-like excitations effectively interacting by means of the usual Coulombic plus a linear confining potential, the latter being related to a string-like excitation binding the monopoles pairs, what indicates that the fractionalization of magnetic dipoles may not be so easy in two dimensions. These findings contrast this material with the three-dimensional analogue, where such monopoles experience only the Coulombic interaction. We discuss, however, two entropic effects that affect the monopole interactions: firstly, the string configurational entropy may loose the string tension and then, free magnetic monopoles should also be found in lower dimensional spin ices; secondly, in contrast to the string configurational entropy, an entropically driven Coulomb force, which increases with temperature, has the opposite effect of confining the magnetic defects.Comment: 8 pages. Accepted by Journal of Applied Physics (2009

Search for Planetary Candidates within the OGLE Stars

We propose a method to distinguish between planetary and stellar companions to stars which present a periodic decrease in brightness, interpreted as a transit. Light curves from a total of 177 stars from the OGLE project were fitted by the model which simulates planetary transits using an opaque disk in front of an image of the Sun. The simulation results yield the orbital radius in units of stellar radii, the orbital inclination angle, and the ratio of the planet to the star radii. Combining Kepler's third law with a mass-radius relation for main sequence stars, it was possible to estimate values for the masses and radii of both the primary and secondary objects. This model was successfully tested with the confirmed planets orbiting the stars HD 209458, TrES-1, OGLE-TR-10, 56, 111, 113, and 132. The method consists of selecting as planetary candidates only those objects with primary densities between 0.7 and 2.3 solar densities (F, G, and K stars) and secondaries with radius less than 1.5 Jupiter radius. The method is not able to distinguish between a planet and a dwarf star with mass less than 0.1 $M_\odot$, such as OGLE-TR-122. We propose a selection of 28 planetary candidates (OGLE-TR-49, 51, 55, 63, 71, 76, 90, 97, 100, 109, 114, 127, 130, 131, 134, 138, 140, 146, 151, 155, 159, 164, 165, 169, 170, 171, 172, and 174) for high resolution spectroscopy follow up.Comment: 4 figures, 2 table

Dipole-induced vortex ratchets in superconducting films with arrays of micromagnets

We investigate the transport properties of superconducting films with periodic arrays of in-plane magnetized micromagnets. Two different magnetic textures are studied: a square array of magnetic bars and a close-packed array of triangular microrings. As confirmed by MFM imaging, the magnetic state of both systems can be adjusted to produce arrays of almost point-like magnetic dipoles. By carrying out transport measurements with ac drive, we observed experimentally a recently predicted ratchet effect induced by the interaction between superconducting vortices and the magnetic dipoles. Moreover, we find that these magnetic textures produce vortex-antivortex patterns, which have a crucial role on the transport properties of this hybrid system.Comment: 4 pages, 4 figure