Transition Temperature of a Uniform Imperfect Bose Gas

We calculate the transition temperature of a uniform dilute Bose gas with repulsive interactions, using a known virial expansion of the equation of state. We find that the transition temperature is higher than that of an ideal gas, with a fractional increase K_0(na^3)^{1/6}, where n is the density and a is the S-wave scattering length, and K_0 is a constant given in the paper. This disagrees with all existing results, analytical or numerical. It agrees exactly in magnitude with a result due to Toyoda, but has the opposite sign.Comment: Email correspondence to [email protected] ; 2 pages using REVTe

The effect of disorder on the critical temperature of a dilute hard sphere gas

We have performed Path Integral Monte Carlo (PIMC) calculations to determine the effect of quenched disorder on the superfluid density of a dilute 3D hard sphere gas. The disorder was introduced by locating set of hard cylinders randomly inside the simulation cell. Our results indicate that the disorder leaves the superfluid critical temperature basically unchanged. Comparison to experiments of helium in Vycor is made.Comment: 4 pages, 4 figure

Transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount \Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where a_{scatt} is the scattering length and n is the density. There have been several different theoretical estimates for the numerical coefficient #. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) phi^4 field theory in three dimensions---an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce non-universal quantities such as the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to improvement of analysis in the longer companion pape

Bose-Einstein Condensation Temperature of Homogenous Weakly Interacting Bose Gas in Variational Perturbation Theory Through Six Loops

We compute the shift of the transition temperature for a homogenous weakly interacting Bose gas in leading order in the scattering length a for given particle density n. Using variational perturbation theory through six loops in a classical three-dimensional scalar field theory, we obtain Delta T_c/T_c = 1.25+/-0.13 a n^(1/3), in agreement with recent Monte-Carlo results.Comment: 4 pages; omega' corrected: final result changes slightly to 1.25+/-0.13; references added; several minor change

Modelling state-dependent interference in common cranes

1. Interference is a key component of food competition, but is difficult to measure in natural animal populations. Using data from a long-term study, we show that interference between common cranes Grus grus L., feeding on patches of cereal seeds, reduces intake rates at high competitor densities, and that the strength of interference is unrelated to food abundance. 2. An alternative to measuring interference directly is to predict its strength using behaviour-based models. We test an interference model, originally developed for shorebirds feeding on invertebrate prey, for cranes. We compare the predictions of a rate-maximizing model, in which animals steal food if this increases intake rate, and a state-dependent model, in which they only rate-maximize if their intake rate is below a target value, otherwise they minimize injury risk by not stealing food. State-dependent aggression occurs in cranes. 3. The state-dependent model predicts more accurately the relative aggression rates of cranes of different dominance. However, both models predict accurately the observed strength of interference, that the strength of interference is unrelated to food abundance, at least within the observed range of crane and seed densities, and that cranes of a higher dominance have a higher intake rate than those of lower dominance. 4. This paper shows how state-dependent behaviour can be incorporated into an interference model, and that the model can produce accurate predictions for a system quite different to that for which it was developed.RAS was funded by the Natural Environment Research Council. LMB was partially funded by Ministerio de Ciencia y Tecnología (MCyT) and research grant PB97-1252 of MCyT. Field work was funded by DGICYT project PB87-0389 of the MCyT.Peer reviewe

The leaching of natural colloids from forest surface soils and their role for the P transfer

Soil nanoparticles (d<100nm) and colloids (d<1µm) exert a decisive control on the mobilisation of strongly sorbing compounds such as phosphorus (P). We investigated the nanoparticles and colloids present in forest soil leachates examining their role for the P fixation and for the vertical P transfer in forest soils. Mesocosm experiments with three German forest soils (upper 20 cm) were conducted. The mesocosms were irrigated with artificial rain for 22 months and the nanoparticles and colloids were characterised in the soil leachates with special attention to P. The field flow fractionation (FFF) technique coupled online to UV- and DLS- detectors and inductively coupled plasma mass spectrometry (ICP-MS) or to an organic carbon detector (OCD) enabled a size resolved characterization and quantification of the nanoparticulate and colloidal fractions and their elemental composition (P, Corg, Fe, A, Si, Ca. Mn). To visualise and better characterise the particles present in the leachates, transmission electron microscopy with energy-dispersive x-ray spectroscopy (TEM-EDX) measurements were performed. The translocated particles exhibited sizes up to 350 nm. Using FFF we separated the colloids in three size fractions i) 3-20 nm ii) 20-70 nm and iii) 70-350 nm. The particle fractions showed different chemical compositions. However their composition and characteristics were similar between the three forest sites and comparable to the natural nanoparticles and colloids from soils (“water dispersible colloids”) and streams described in literature. Up to 90% (on average ~45 %) of the leached P was associated with the nanoparticles and colloids. Our qualitative and quantitative analysis of the soil leachates showed that nanoparticles and colloids are crucial vectors controlling the P fluxes in forest ecosystems and could be a significant, but as yet still poorly quantified P loss factor

Quantum corrections to the ground state energy of a trapped Bose-Einstein condensate: A diffusion Monte Carlo calculation

The diffusion Monte Carlo method is applied to describe a trapped atomic Bose-Einstein condensate at zero temperature, fully quantum mechanically and nonperturbatively. For low densities, $n(0)a^3 \le 2 \cdot 10^{-3}$ [n(0): peak density, a: s-wave scattering length], our calculations confirm that the exact ground state energy for a sum of two-body interactions depends on only the atomic physics parameter a, and no other details of the two-body model potential. Corrections to the mean-field Gross-Pitaevskii energy range from being essentially negligible to about 20% for N=2-50 particles in the trap with positive s-wave scattering length a=100-10000 a.u.. Our numerical calculations confirm that inclusion of an additional effective potential term in the mean-field equation, which accounts for quantum fluctuations [see e.g. E. Braaten and A. Nieto, Phys. Rev. B 56}, 14745 (1997)], leads to a greatly improved description of trapped Bose gases.Comment: 7 pages, 4 figure

The density dependence of the transition temperature in a homogenous Bose flui

Transition temperature data obtained as a function of particle density in the $^4$He-Vycor system are compared with recent theoretical calculations for 3D Bose condensed systems. In the low density dilute Bose gas regime we find, in agreement with theory, a positive shift in the transition temperature of the form $\Delta T/T_0 = \gamma(na^{3})^{1/3}$. At higher densities a maximum is found in the ratio of $T_c /T_0$ for a value of the interaction parameter, na$^3$, that is in agreement with path-integral Monte Carlo calculations.Comment: 4 pages, 3 figure

Thermodynamics of a trapped interacting Bose gas and the renormalization group

We apply perturbative renormalization group theory to the symmetric phase of a dilute interacting Bose gas which is trapped in a three-dimensional harmonic potential. Using Wilsonian energy-shell renormalization and the epsilon-expansion, we derive the flow equations for the system. We relate these equations to the flow for the homogeneous Bose gas. In the thermodynamic limit, we apply our results to study the transition temperature as a function of the scattering length. Our results compare well to previous studies of the problem.Comment: 14 pages, 5 figure

Thermodynamic properties of confined interacting Bose gases - a renormalization group approach

A renormalization group method is developed with which thermodynamic properties of a weakly interacting, confined Bose gas can be investigated. Thereby effects originating from a confining potential are taken into account by periodic boundary conditions and by treating the resulting discrete energy levels of the confined degrees of freedom properly. The resulting density of states modifies the flow equations of the renormalization group in momentum space. It is shown that as soon as the characteristic length of confinement becomes comparable to the thermal wave length of a weakly interacting and trapped Bose gas its thermodynamic properties are changed significantly. This is exemplified by investigating characteristic bunching properties of the interacting Bose gas which manifest themselves in the second order coherence factor