Geometric Phase and Modulo Relations for Probability Amplitudes as Functions on Complex Parameter Spaces

We investigate general differential relations connecting the respective behavior s of the phase and modulo of probability amplitudes of the form \amp{\psi_f}{\psi}, where $\ket{\psi_f}$ is a fixed state in Hilbert space and $\ket{\psi}$ is a section of a holomorphic line bundle over some complex parameter space. Amplitude functions on such bundles, while not strictly holomorphic, nevertheless satisfy generalized Cauchy-Riemann conditions involving the U(1) Berry-Simon connection on the parameter space. These conditions entail invertible relations between the gradients of the phase and modulo, therefore allowing for the reconstruction of the phase from the modulo (or vice-versa) and other conditions on the behavior of either polar component of the amplitude. As a special case, we consider amplitude functions valued on the space of pure states, the ray space ${\cal R} = {\mathbb C}P^n$, where transition probabilities have a geometric interpretation in terms of geodesic distances as measured with the Fubini-Study metric. In conjunction with the generalized Cauchy-Riemann conditions, this geodesic interpretation leads to additional relations, in particular a novel connection between the modulus of the amplitude and the phase gradient, somewhat reminiscent of the WKB formula. Finally, a connection with geometric phases is established.Comment: 11 pages, 1 figure, revtex

Field experimental study of traffic-induced turbulence on highways

This paper is focused on traffic-induced turbulence (TIT) analysis from a field campaign performed in 2011, using ultrasonic anemometers deployed in the M-12 Highways, Madrid (Spain). The study attempts to improve knowledge about the influence of traffic-related parameters on turbulence. Linear relationships between vehicle speed and turbulent kinetic energy (TKE) values are found with coefficients of determination (R2) of 0.75 and 0.55 for the lorry and van respectively. The vehicle-induced fluctuations in the wind components (u', v' and w') showed the highest values for the longitudinal component (v) because of the wake-passing effect. In the analysis of wake produced by moving vehicles it is indicated how the turbulence dissipates in relation to a distance d and height h. The TKE values were found to be higher at the measuring points closer to the surface during the wake analysis.This work was supported by the OASIS Research Project that was co financed by CDTI (Spanish Science and Innovation Ministry) and developed with the Spanish companies: Iridium, OHL Concesiones, Abertis, Sice, Indra, Dragados, OHL, Geocisa, GMV, Asfaltos Augusta, Hidrofersa, Eipsa, PyG, CPS, AEC and Torre de Comares Arquitectos s.l and 16 research centres

The Multitude of Unresolved Continuum Sources at 1.6 microns in Hubble Space Telescope images of Seyfert Galaxies

We examine 112 Seyfert galaxies observed by the Hubble Space Telescope (HST) at 1.6 microns. We find that ~50% of the Seyfert 2.0 galaxies which are part of the Revised Shapeley-Ames (RSA) Catalog or the CfA redshift sample contain unresolved continuum sources at 1.6 microns. All but a couple of the Seyfert 1.0-1.9 galaxies display unresolved continuum sources. The unresolved sources have fluxes of order a mJy, near-infrared luminosities of order 10^41 erg/s and absolute magnitudes M_H ~-16. Comparison non-Seyfert galaxies from the RSA Catalog display significantly fewer (~20%), somewhat lower luminosity nuclear sources, which could be due to compact star clusters. We find that the luminosities of the unresolved Seyfert 1.0-1.9 sources at 1.6 microns are correlated with [OIII] 5007A and hard X-ray luminosities, implying that these sources are non-stellar. Assuming a spectral energy distribution similar to that of a Seyfert 2 galaxy, we estimate that a few percent of local spiral galaxies contain black holes emitting as Seyferts at a moderate fraction, 10^-1 to 10^-4, of their Eddington luminosities. With increasing Seyfert type the fraction of unresolved sources detected at 1.6 microns and the ratio of 1.6 microns to [OIII] fluxes tend to decrease. These trends are consistent with the unification model for Seyfert 1 and 2 galaxies.Comment: accepted by Ap

Blue Dots Team Transits Working Group Review

Transiting planet systems offer an unique opportunity to observationally constrain proposed models of the interiors (radius, composition) and atmospheres (chemistry, dynamics) of extrasolar planets. The spectacular successes of ground-based transit surveys (more than 60 transiting systems known to-date) and the host of multi-wavelength, spectro-photometric follow-up studies, carried out in particular by HST and Spitzer, have paved the way to the next generation of transit search projects, which are currently ongoing (CoRoT, Kepler), or planned. The possibility of detecting and characterizing transiting Earth-sized planets in the habitable zone of their parent stars appears tantalizingly close. In this contribution we briefly review the power of the transit technique for characterization of extrasolar planets, summarize the state of the art of both ground-based and space-borne transit search programs, and illustrate how the science of planetary transits fits within the Blue Dots perspective.Comment: 9 pages, 3 figures, to be published in the proceedings (ASP Conf. Ser.) of the "Pathways Towards Habitable Planets" conference, held in Barcelona (14-18 Sep 2009

On domain walls in a Ginzburg-Landau non-linear S^2-sigma model

The domain wall solutions of a Ginzburg-Landau non-linear $S^2$-sigma hybrid model are unveiled. There are three types of basic topological walls and two types of degenerate families of composite - one topological, the other non-topological- walls. The domain wall solutions are identified as the finite action trajectories (in infinite time) of a related mechanical system that is Hamilton-Jacobi separable in sphero-conical coordinates. The physical and mathematical features of these domain walls are thoroughly discussed.Comment: 26 pages, 18 figure

Higher Dimensional Taub-NUTs and Taub-Bolts in Einstein-Maxwell Gravity

We present a class of higher dimensional solutions to Einstein-Maxwell equations in d-dimensions. These solutions are asymptotically locally flat, de-Sitter, or anti-de Sitter space-times. The solutions we obtained depend on two extra parameters other than the mass and the nut charge. These two parameters are the electric charge, q and the electric potential at infinity, V, which has a non-trivial contribution. We Analyze the conditions one can impose to obtain Taub-Nut or Taub-Bolt space-times, including the four-dimensional case. We found that in the nut case these conditions coincide with that coming from the regularity of the one-form potential at the horizon. Furthermore, the mass parameter for the higher dimensional solutions depends on the nut charge and the electric charge or the potential at infinity.Comment: 11 pages, LaTe

Dynamics of zonal flow-like structures in the edge of the TJ-II stellarator

The dynamics of fluctuating electric field structures in the edge of the TJ-II stellarator, that display zonal flow-like traits, is studied. These structures have been shown to be global and affect particle transport dynamically [J.A. Alonso et al., Nucl. Fus. 52 063010 (2012)]. In this article we discuss possible drive (Reynolds stress) and damping (Neoclassical viscosity, geodesic transfer) mechanisms for the associated ExB velocity. We show that: (a) while the observed turbulence-driven forces can provide the necessary perpendicular acceleration, a causal relation could not be firmly established, possibly because of the locality of the Reynolds stress measurements, (b) the calculated neoclassical viscosity and damping times are comparable to the observed zonal flow relaxation times, and (c) although an accompanying density modulation is observed to be associated to the zonal flow, it is not consistent with the excitation of pressure side-bands, like those present in geodesic acoustic oscillations, caused by the compression of the ExB flow field