Quantum Numbers for Excitations of Bose-Einstein Condensates in 1D Optical Lattices

The excitation spectrum and the band structure of a Bose-Einstein condensate in a periodic potential are investigated. Analyses within full 3D systems, finite 1D systems, and ideal periodic 1D systems are compared. We find two branches of excitations in the spectra of the finite 1D model. The band structures for the first and (part of) the second band are compared between a finite 1D and the fully periodic 1D systems, utilizing a new definition of a effective wavenumber and a phase-slip number. The upper and lower edges of the first gap coincide well between the two cases. The remaining difference is explained by the existence of the two branches due to the finite-size effect.Comment: 5 pages, 9 figure

Radio Afterglows of Gamma-Ray Bursts and Hypernovae at High Redshift, and their Potential for 21-cm Absorption Studies

We investigate the radio afterglows of gamma-ray bursts (GRBs) and hypernovae (HNe) at high redshifts and quantify their detectability, as well as their potential usefulness for 21 cm absorption line studies of the intergalactic medium (IGM) and intervening structures. We examine several sets of source and environment model parameters that are physically plausible at high redshifts. The radio afterglows of GRBs would be detectable out to z ~ 30, while the energetic HNe could be detectable out to z ~ 20 even by the current Very Large Array (VLA). We find that the 21 cm absorption line due to the diffuse neutral IGM is difficult to detect even by the proposed Square Kilometer Array (SKA), except for highly energetic sources. We also find that the 21 cm line due to collapsed gas clouds with high optical depth may be detected on rare occasions.Comment: 36 pages, 12 figures, 1 table, accepted for publication in Ap

A λ = 1.3 Millimeter Aperture Synthesis Molecular Line Survey of Orion Kleinmann-Low

We present a 1".3 spatial resolution interferometric spectral line survey of the core of the Orion molecular cloud, obtained with the OVRO millimeter array. Covering 4 GHz bandwidth in total, the survey contains ~100 emission lines from 18 chemical species. The spatial distributions of a number of molecules point to source I near the IRc2 complex as the dominant energy source in the region but do not rule out the presence of additional lower luminosity objects. At arcsecond resolution, the offsets between dust emission and various molecular tracers suggest that the spectacular "hot core" emission in the Orion core arises via the heating and ablation of material from the surfaces of very high density clumps located ≳500 AU from source I and traced by the dust emission. We find no evidence for a strong internal heating source within the hot core condensation(s)

A Co-moving Coordinate System for Relativistic Hydrodynamics

The equations of relativistic hydrodynamics are transformed so that steps forward in time preserves local simultaneity. In these variables, the space-time coordinates of neighboring points on the mesh are simultaneous according to co-moving observers. Aside from the time step varying as a function of the location on the mesh, the local velocity gradient and the local density then evolve according to non-relativistic equations of motion. Analytic solutions are found for two one-dimensional cases with constant speed of sound. One solution has a Gaussian density profile when mapped into the new coordinates. That solution is analyzed for the effects of longitudinal acceleration in relativistic heavy ion collisions at RHIC, especially in regards to two-particle correlation measurements of the longitudinal size

The Hubbard model on a complete graph: Exact Analytical results

We derive the analytical expression of the ground state of the Hubbard model with unconstrained hopping at half filling and for arbitrary lattice sites.Comment: Email:[email protected]

On the Integrability, B\"Acklund Transformation and Symmetry Aspects of a Generalized Fisher Type Nonlinear Reaction-Diffusion Equation

The dynamics of nonlinear reaction-diffusion systems is dominated by the onset of patterns and Fisher equation is considered to be a prototype of such diffusive equations. Here we investigate the integrability properties of a generalized Fisher equation in both (1+1) and (2+1) dimensions. A Painlev\'e singularity structure analysis singles out a special case ($m=2$) as integrable. More interestingly, a B\"acklund transformation is shown to give rise to a linearizing transformation for the integrable case. A Lie symmetry analysis again separates out the same $m=2$ case as the integrable one and hence we report several physically interesting solutions via similarity reductions. Thus we give a group theoretical interpretation for the system under study. Explicit and numerical solutions for specific cases of nonintegrable systems are also given. In particular, the system is found to exhibit different types of travelling wave solutions and patterns, static structures and localized structures. Besides the Lie symmetry analysis, nonclassical and generalized conditional symmetry analysis are also carried out.Comment: 30 pages, 10 figures, to appear in Int. J. Bifur. Chaos (2004

Saddles in the energy landscape: extensivity and thermodynamic formalism

We formally extend the energy landscape approach for the thermodynamics of liquids to account for saddle points. By considering the extensive nature of macroscopic potential energies, we derive the scaling behavior of saddles with system size, as well as several approximations for the properties of low-order saddles (i.e., those with only a few unstable directions). We then cast the canonical partition function in a saddle-explicit form and develop, for the first time, a rigorous energy landscape approach capable of reproducing trends observed in simulations, in particular the temperature dependence of the energy and fractional order of sampled saddles.Comment: 4 pages, 1 figur

Can hypnotic suggestibility be measured online?

Hypnosis and hypnotic suggestions are gradually gaining popularity within the consciousness community as established tools for the experimental manipulation of illusions of involuntariness, hallucinations and delusions. However, hypnosis is still far from being a widespread instrument; a crucial hindrance to taking it up is the amount of time needed to invest in identifying people high and low in responsiveness to suggestion. In this study, we introduced an online assessment of hypnotic response and estimated the extent to which the scores and psychometric properties of an online screening differ from an offline one. We propose that the online screening of hypnotic response is viable as it reduces the level of responsiveness only by a slight extent. The application of online screening may prompt researchers to run large-scale studies with more heterogeneous samples, which would help researchers to overcome some of the issues underlying the current replication crisis in psychology

Cross-Correlation Studies between CMB Temperature Anisotropies and 21 cm Fluctuations

During the transition from a neutral to a fully reionized universe, scattering of cosmic microwave background (CMB) photons via free-electrons leads to a new anisotropy contribution to the temperature distribution. If the reionization process is inhomogeneous and patchy, the era of reionization is also visible via brightness temperature fluctuations in the redshifted 21 cm line emission from neutral Hydrogen. Since regions containing electrons and neutral Hydrogen are expected to trace the same underlying density field, the two are (anti) correlated and this is expected to be reflected in the anisotropy maps via a correlation between arcminute-scale CMB temperature and the 21 cm background. In terms of the angular cross-power spectrum, unfortunately, this correlation is insignificant due to a geometric cancellation associated with second order CMB anisotropies. The same cross-correlation between ionized and neutral regions, however, can be studied using a bispectrum involving large scale velocity field of ionized regions from the Doppler effect, arcminute scale CMB anisotropies during reionization, and the 21 cm background. While the geometric cancellation is partly avoided, the signal-to-noise ratio related to this bispectrum is reduced due to the large cosmic variance related to velocity fluctuations traced by the Doppler effect. Unless the velocity field during reionization can be independently established, it is unlikely that the correlation information related to the relative distribution of ionized electrons and regions containing neutral Hydrogen can be obtained with a combined study involving CMB and 21 cm fluctuations.Comment: 10 pages, 3 figure

Thermophoresis of Brownian particles driven by coloured noise

The Brownian motion of microscopic particles is driven by the collisions with the molecules of the surrounding fluid. The noise associated with these collisions is not white, but coloured due, e.g., to the presence of hydrodynamic memory. The noise characteristic time scale is typically of the same order as the time over which the particle's kinetic energy is lost due to friction (inertial time scale). We demonstrate theoretically that, in the presence of a temperature gradient, the interplay between these two characteristic time scales can have measurable consequences on the particle long-time behaviour. Using homogenization theory, we analyse the infinitesimal generator of the stochastic differential equation describing the system in the limit where the two characteristic times are taken to zero; from this generator, we derive the thermophoretic transport coefficient, which, we find, can vary in both magnitude and sign, as observed in experiments. Furthermore, studying the long-term stationary particle distribution, we show that particles can accumulate towards the colder (positive thermophoresis) or the warmer (negative thermophoresis) regions depending on the dependence of their physical parameters and, in particular, their mobility on the temperature.Comment: 9 pages, 4 figure