Implications of Lorentz covariance for the guidance equation in two-slit quantum interference

It is known that Lorentz covariance fixes uniquely the current and the associated guidance law in the trajectory interpretation of quantum mechanics for spin particles. In the non-relativistic domain this implies a guidance law for the electron which differs by an additional spin-dependent term from that originally proposed by de Broglie and Bohm. In this paper we explore some of the implications of the modified guidance law. We bring out a property of mutual dependence in the particle coordinates that arises in product states, and show that the quantum potential has scalar and vector components which implies the particle is subject to a Lorentz-like force. The conditions for the classical limit and the limit of negligible spin are given, and the empirical sufficiency of the model is demonstrated. We then present a series of calculations of the trajectories based on two-dimensional Gaussian wave packets which illustrate how the additional spin-dependent term plays a significant role in structuring both the individual trajectories and the ensemble. The single packet corresponds to quantum inertial motion. The distinct features encountered when the wavefunction is a product or a superposition are explored, and the trajectories that model the two-slit experiment are given. The latter paths exhibit several new characteristics compared with the original de Broglie-Bohm ones, such as crossing of the axis of symmetry.Comment: 27 pages including 6 pages of figure

Bohmian trajectories and Klein's paradox

We compute the Bohmian trajectories of the incoming scattering plane waves for Klein's potential step in explicit form. For finite norm incoming scattering solutions we derive their asymptotic space-time localization and we compute some Bohmian trajectories numerically. The paradox, which appears in the traditional treatments of the problem based on the outgoing scattering asymptotics, is absent.Comment: 14 pages, 3 figures; minor format change

HST/STIS Imaging of the Host Galaxy of GRB980425/SN1998bw

We present HST/STIS observations of ESO 184-G82, the host galaxy of the gamma-ray burst GRB 980425 associated with the peculiar Type Ic supernova SN1998bw. ESO 184-G82 is found to be an actively star forming SBc sub-luminous galaxy. We detect an object consistent with being a point source within the astrometric uncertainty of 0.018 arcseconds of the position of the supernova. The object is located inside a star-forming region and is at least one magnitude brighter than expected for the supernova based on a simple radioactive decay model. This implies either a significant flattening of the light curve or a contribution from an underlying star cluster.Comment: 12 pages, 2 figures, AASTeX v5.02 accepted for publication in ApJ Letter

Comments on the Quantum Potential Approach to a Class of Quantum Cosmological Models

In this comment we bring attention to the fact that when we apply the ontological interpretation of quantum mechanics, we must be sure to use it in the coordinate representation. This is particularly important when canonical tranformations that mix momenta and coordinates are present. This implies that some of the results obtained by A. B\l aut and J. Kowalski-Glikman are incorrect.Comment: 7 pages, LaTe

An Updated Ultraviolet Calibration for the Swift/UVOT

We present an updated calibration of the Swift/UVOT broadband ultraviolet (uvw1, uvm2, and uvw2) filters. The new calibration accounts for the ~1% per year decline in the UVOT sensitivity observed in all filters, and makes use of additional calibration sources with a wider range of colours and with HST spectrophotometry. In this paper we present the new effective area curves and instrumental photometric zeropoints and compare with the previous calibration.Comment: 4 pages, 3 figures, 2 tables. Presented at GRB 2010 symposium, Annapolis, November 2010 to be published in American Institute of Physics Conference Serie

Hierarchical Models for Independence Structures of Networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.Comment: 19 pages, 7 figure