Proof of Bose-Einstein Condensation for Dilute Trapped Gases

The ground state of bosonic atoms in a trap has been shown experimentally to display Bose-Einstein condensation (BEC). We prove this fact theoretically for bosons with two-body repulsive interaction potentials in the dilute limit, starting from the basic Schroedinger equation; the condensation is 100% into the state that minimizes the Gross-Pitaevskii energy functional. This is the first rigorous proof of BEC in a physically realistic, continuum model.Comment: Revised version with some simplifications and clarifications. To appear in Phys. Rev. Let

Abrupt grain boundary melting in ice

The effect of impurities on the grain boundary melting of ice is investigated through an extension of Derjaguin-Landau-Verwey-Overbeek theory, in which we include retarded potential effects in a calculation of the full frequency dependent van der Waals and Coulombic interactions within a grain boundary. At high dopant concentrations the classical solutal effect dominates the melting behavior. However, depending on the amount of impurity and the surface charge density, as temperature decreases, the attractive tail of the dispersion force interaction begins to compete effectively with the repulsive screened Coulomb interaction. This leads to a film-thickness/temperature curve that changes depending on the relative strengths of these interactions and exhibits a decrease in the film thickness with increasing impurity level. More striking is the fact that at very large film thicknesses, the repulsive Coulomb interaction can be effectively screened leading to an abrupt reduction to zero film thickness.Comment: 8 pages, 1 figur

Some comments on developments in exact solutions in statistical mechanics since 1944

Lars Onsager and Bruria Kaufman calculated the partition function of the Ising model exactly in 1944 and 1949. Since then there have been many developments in the exact solution of similar, but usually more complicated, models. Here I shall mention a few, and show how some of the latest work seems to be returning once again to the properties observed by Onsager and Kaufman.Comment: 28 pages, 5 figures, section on six-vertex model revise

U(1) Gauge Theory as Quantum Hydrodynamics

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.Comment: 15 pages, Plain LaTeX, final published versio

Digestive environments of benthic macroinvertebrate guts: Enzymes, surfactants and dissolved organic matter

Hydrolytic enzyme activity, surfactancy, and dissolved organic matter in the digestive lumens of 19 benthic echinoderm and polychaete species were examined, using consistent and quantifiable methods. Enzyme activities were compared with those of extracellular enzymes from ambient sediments. Enzyme activities ranged over five orders of magnitude, with averages decreasing in the order polychaetes \u3e echinoderms \u3e sediment. Highest activities in animals were usually associated with the fluid phase in midgut sections, with posteriorward decreases indicating little export to the external environment. At some phyletic levels, activity correlated inversely with animal size. Hydrolase patterns reflected food type; for example, high lipase:protease ratios in carnivores reflected esterified lipids in their diets. High surfactant activity was found in gut sections having high enzyme activity. Deposit feeders had the most intense surfactancy, including evidence for micelles. While enzymes reflected the biochemical nature of the digestible food substrate regardless of feeding mode (e.g., deposit vs. suspension feeder), surfactants reflected dilution of this digestible substrate with mineral grains. Dissolved organic matter levels were high, with amino acids reaching levels \u3e 1M and lipids commonly 1 g L−1. Among polychaete deposit-feeders, low molecular weight amino acids reflected the composition of the food substrate, but were present at much higher concentrations than could be explained by sediment present in the gut—suggesting longer residence times for fluid than for transiting sediment particles. Deposit feeder digestive fluids are better able to solubilize sedimentary food substrates than are sedimentary extracellular enzymes, owing to either more powerful solubilizing agents or to their deployment in freely diffusing, dissolved form. Gut environments may lead to chemical condensation as well as solubilization reactions

Single vibronic level emission spectroscopic studies of the ground state energy levels and molecular structures of jet-cooled HGeBr, DGeBr, HGeI, and DGeI

Single vibronic level dispersed fluorescence spectra of jet-cooled HGeBr, DGeBr, HGeI, and DGeI have been obtained by laser excitation of selected bands of the à A″1-X̃ A′1 electronic transition. The measured ground state vibrational intervals were assigned and fitted to anharmonicity expressions, which allowed the harmonic frequencies to be determined for both isotopomers. In some cases, lack of a suitable range of emission data necessitated that some of the anharmonicity constants and vibrational frequencies be estimated from those of HGeCl∕DGeCl and the corresponding silylenes (HSiX). Harmonic force fields were obtained for both molecules, although only four of the six force constants could be determined. The ground state effective rotational constants and force field data were combined to calculate average (rz) and approximate equilibrium (rze) structures. For HGeBr rze(GeH)=1.593(9)Å, rze(GeBr)=2.325(21)Å, and the bond angle was fixed at our CCSD(T)/aug-cc-pVTZ ab initio value of 93.6°. For HGeI we obtained rze(GeH)=1.589(1)Å, rze(GeI)=2.525(5)Å, and bond angle=93.2°. Franck-Condon simulations of the emission spectra using ab initio Cartesian displacement coordinates reproduce the observed intensity distributions satisfactorily. The trends in structural parameters in the halogermylenes and halosilylenes can be readily understood based on the electronegativity of the halogen substituent. ACKNOWLEDGMENT

Incorporating interactive 3-dimensional graphics in astronomy research papers

Most research data collections created or used by astronomers are intrinsically multi-dimensional. In contrast, all visual representations of data presented within research papers are exclusively 2-dimensional. We present a resolution of this dichotomy that uses a novel technique for embedding 3-dimensional (3-d) visualisations of astronomy data sets in electronic-format research papers. Our technique uses the latest Adobe Portable Document Format extensions together with a new version of the S2PLOT programming library. The 3-d models can be easily rotated and explored by the reader and, in some cases, modified. We demonstrate example applications of this technique including: 3-d figures exhibiting subtle structure in redshift catalogues, colour-magnitude diagrams and halo merger trees; 3-d isosurface and volume renderings of cosmological simulations; and 3-d models of instructional diagrams and instrument designs.Comment: 18 pages, 7 figures, submitted to New Astronomy. For paper with 3-dimensional embedded figures, see http://astronomy.swin.edu.au/s2plot/3dpd

From Capillary Condensation to Interface Localization Transitions in Colloid Polymer Mixtures Confined in Thin Film Geometry

Monte Carlo simulations of the Asakura-Oosawa (AO) model for colloid-polymer mixtures confined between two parallel repulsive structureless walls are presented and analyzed in the light of current theories on capillary condensation and interface localization transitions. Choosing a polymer to colloid size ratio of q=0.8 and studying ultrathin films in the range of D=3 to D=10 colloid diameters thickness, grand canonical Monte Carlo methods are used; phase transitions are analyzed via finite size scaling, as in previous work on bulk systems and under confinement between identical types of walls. Unlike the latter work, inequivalent walls are used here: while the left wall has a hard-core repulsion for both polymers and colloids, at the right wall an additional square-well repulsion of variable strength acting only on the colloids is present. We study how the phase separation into colloid-rich and colloid-poor phases occurring already in the bulk is modified by such a confinement. When the asymmetry of the wall-colloid interaction increases, the character of the transition smoothly changes from capillary condensation-type to interface localization-type. The critical behavior of these transitions is discussed, as well as the colloid and polymer density profiles across the film in the various phases, and the correlation of interfacial fluctuations in the direction parallel to the confining walls. The experimental observability of these phenomena also is briefly discussed.Comment: 36 pages, 15 figure

Droplet shapes on structured substrates and conformal invariance

We consider the finite-size scaling of equilibrium droplet shapes for fluid adsorption (at bulk two-phase co-existence) on heterogeneous substrates and also in wedge geometries in which only a finite domain $\Lambda_{A}$ of the substrate is completely wet. For three-dimensional systems with short-ranged forces we use renormalization group ideas to establish that both the shape of the droplet height and the height-height correlations can be understood from the conformal invariance of an appropriate operator. This allows us to predict the explicit scaling form of the droplet height for a number of different domain shapes. For systems with long-ranged forces, conformal invariance is not obeyed but the droplet shape is still shown to exhibit strong scaling behaviour. We argue that droplet formation in heterogeneous wedge geometries also shows a number of different scaling regimes depending on the range of the forces. The conformal invariance of the wedge droplet shape for short-ranged forces is shown explicitly.Comment: 20 pages, 7 figures. (Submitted to J.Phys.:Cond.Mat.