Symmetry Aspects in Nonrelativistic Multi-Scalar Field Models and Application to a Coupled Two-Species Dilute Bose Gas

We discuss unusual aspects of symmetry that can happen due to entropic effects in the context of multi-scalar field theories at finite temperature. We present their consequences, in special, for the case of nonrelativistic models of hard core spheres. We show that for nonrelativistic models phenomena like inverse symmetry breaking and symmetry non-restoration cannot take place, but a reentrant phase at high temperatures is shown to be possible for some region of parameters. We then develop a model of interest in studies of Bose-Einstein condensation in dilute atomic gases and discuss about its phase transition patterns. In this application to a Bose-Einstein condensation model, however, no reentrant phases are found.Comment: 8 pages, 1 eps figure, IOP style. Based on a talk given by R. O. Ramos at the QFEXT05 workshop, Barcelona, Spain, September 5-9, 2005. One reference was update

Effective action in DSR1 quantum field theory

We present the one-loop effective action of a quantum scalar field with DSR1 space-time symmetry as a sum over field modes. The effective action has real and imaginary parts and manifest charge conjugation asymmetry, which provides an alternative theoretical setting to the study of the particle-antiparticle asymmetry in nature.Comment: 8 page

Parameterizing Quasiperiodicity: Generalized Poisson Summation and Its Application to Modified-Fibonacci Antenna Arrays

The fairly recent discovery of "quasicrystals", whose X-ray diffraction patterns reveal certain peculiar features which do not conform with spatial periodicity, has motivated studies of the wave-dynamical implications of "aperiodic order". Within the context of the radiation properties of antenna arrays, an instructive novel (canonical) example of wave interactions with quasiperiodic order is illustrated here for one-dimensional (1-D) array configurations based on the "modified-Fibonacci" sequence, with utilization of a two-scale generalization of the standard Poisson summation formula for periodic arrays. This allows for a "quasi-Floquet" analytic parameterization of the radiated field, which provides instructive insights into some of the basic wave mechanisms associated with quasiperiodic order, highlighting similarities and differences with the periodic case. Examples are shown for quasiperiodic infinite and spatially-truncated arrays, with brief discussion of computational issues and potential applications.Comment: 29 pages, 10 figures. To be published in IEEE Trans. Antennas Propagat., vol. 53, No. 6, June 200

Recording from two neurons: second order stimulus reconstruction from spike trains and population coding

We study the reconstruction of visual stimuli from spike trains, recording simultaneously from the two H1 neurons located in the lobula plate of the fly Chrysomya megacephala. The fly views two types of stimuli, corresponding to rotational and translational displacements. If the reconstructed stimulus is to be represented by a Volterra series and correlations between spikes are to be taken into account, first order expansions are insufficient and we have to go to second order, at least. In this case higher order correlation functions have to be manipulated, whose size may become prohibitively large. We therefore develop a Gaussian-like representation for fourth order correlation functions, which works exceedingly well in the case of the fly. The reconstructions using this Gaussian-like representation are very similar to the reconstructions using the experimental correlation functions. The overall contribution to rotational stimulus reconstruction of the second order kernels - measured by a chi-squared averaged over the whole experiment - is only about 8% of the first order contribution. Yet if we introduce an instant-dependent chi-square to measure the contribution of second order kernels at special events, we observe an up to 100% improvement. As may be expected, for translational stimuli the reconstructions are rather poor. The Gaussian-like representation could be a valuable aid in population coding with large number of neurons