Effective renormalized multi-body interactions of harmonically confined ultracold neutral bosons

We calculate the renormalized effective 2-, 3-, and 4-body interactions for N neutral ultracold bosons in the ground state of an isotropic harmonic trap, assuming 2-body interactions modeled with the combination of a zero-range and energy-dependent pseudopotential. We work to third-order in the scattering length a defined at zero collision energy, which is necessary to obtain both the leading-order effective 4-body interaction and consistently include finite-range corrections for realistic 2-body interactions. The leading-order, effective 3- and 4-body interaction energies are U3 = -(0.85576...)(a/l)^2 + 2.7921(1)(a/l)^3 + O[(a/l)^4] and U4 = +(2.43317...)(a/l)^3 + O[(a\l)^4], where w and l are the harmonic oscillator frequency and length, respectively, and energies are in units of hbar*w. The one-standard deviation error 0.0001 for the third-order coefficient in U3 is due to numerical uncertainty in estimating a slowly converging sum; the other two coefficients are either analytically or numerically exact. The effective 3- and 4-body interactions can play an important role in the dynamics of tightly confined and strongly correlated systems. We also performed numerical simulations for a finite-range boson-boson potential, and it was comparison to the zero-range predictions which revealed that finite-range effects must be taken into account for a realistic third-order treatment. In particular, we show that the energy-dependent pseudopotential accurately captures, through third order, the finite-range physics, and in combination with the multi-body effective interactions gives excellent agreement with the numerical simulations, validating our theoretical analysis and predictions.Comment: Updated introduction, correction of a few typos and sign error

Empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular jacobians of genus 2 curves

This paper provides empirical evidence for the Birch and Swinnerton-Dyer conjectures for modular Jacobians of genus 2 curves. The second of these conjectures relates six quantities associated to a Jacobian over the rational numbers. One of these six quantities is the size of the Shafarevich-Tate group. Unable to compute that, we computed the five other quantities and solved for the last one. In all 32 cases, the result is very close to an integer that is a power of 2. In addition, this power of 2 agrees with the size of the 2-torsion of the Shafarevich-Tate group, which we could compute

Are the distributions of Fast Radio Burst properties consistent with a cosmological population?

High time resolution radio surveys over the last few years have discovered a population of millisecond-duration transient bursts called Fast Radio Bursts (FRBs), which remain of unknown origin. FRBs exhibit dispersion consistent with propagation through a cold plasma and dispersion measures indicative of an origin at cosmological distances. In this paper we perform Monte Carlo simulations of a cosmological population of FRBs, based on assumptions consistent with observations of their energy distribution, their spatial density as a function of redshift and the properties of the interstellar and intergalactic media. We examine whether the dispersion measures, fluences, inferred redshifts, signal-to-noises and effective widths of known FRBs are consistent with a cosmological population. Statistical analyses indicate that at least 50 events at Parkes are required to distinguish between a constant co-moving FRB density, and a FRB density that evolves with redshift like the cosmological star formation rate density.Comment: 11 pages, 7 figures, 3 table

Pharmacy-led implementation of evidence based medicine in primary care : Evaluating Diuretics in Usual Care study (EVIDENCE)

Introduction Obtaining evidence of comparative effectiveness and safety of widely prescribed drugs in a timely cost-effective way is emerging as a major global challenge for healthcare systems. The Evaluating Drugs in Normal Care (EVIDENCE) programme addresses this challenge through novel methodology. We describe an exemplar pilot study comparing thiazide type diuretics for hypertension. Method Patients prescribed either indapamide or bendroflumethiazide for hypertension were identified in each primary care practice recruited. Random allocation of a prescribing policy for one or other of these drugs was then applied to the whole practice and where required repeat prescriptions were switched to comply with randomised policy. Patients were informed of the potential switch by letter with the option to discuss further with the study team and/or opt-out of the switch. Routinely collected hospitalization and death data in NHS will be used to compare cardiovascular event rates between the two policies. Results We found bendroflumethiazide was prescribed to 78% of patients prescribed either of these drugs despite recent NICE preference for indapamide. 29 primary care practices in 5 Scottish NHS boards were recruited and 14 randomised to indapamide and 15 to bendroflumethiazide creating a study population of 5985 patients. Less than 0.23% of patients opted out. Conclusion This pilot study demonstrated the feasibility and cost efficiency of the EVIDENCE approach. A relatively large study was generated rapidly with negligible disruption to practice workflows. EVIDENCE methodology offers a novel way to compare the effectiveness of a wide range of medicines where there is clinical equipoise.Non peer reviewe

Relativistic spin precession in the binary PSR J1141−-6545

PSR J1141$-$6545 is a precessing binary pulsar that has the rare potential to reveal the two-dimensional structure of a non-recycled pulsar emission cone. It has undergone $\sim 25 \deg$ of relativistic spin precession in the $\sim18$ years since its discovery. In this paper, we present a detailed Bayesian analysis of the precessional evolution of the width of the total intensity profile, to understand the changes to the line-of-sight impact angle ($\beta$) of the pulsar using four different physically motivated prior distribution models. Although we cannot statistically differentiate between the models with confidence, the temporal evolution of the linear and circular polarisations strongly argue that our line-of-sight crossed the magnetic pole around MJD 54000 and that only two models remain viable. For both these models, it appears likely that the pulsar will precess out of our line-of-sight in the next $3-5$ years, assuming a simple beam geometry. Marginalising over $\beta$ suggests that the pulsar is a near-orthogonal rotator and provides the first polarization-independent estimate of the scale factor ($\mathbb{A}$) that relates the pulsar beam opening angle ($\rho$) to its rotational period ($P$) as $\rho = \mathbb{A}P^{-0.5}$ : we find it to be $> 6 \rm~deg~s^{0.5}$ at 1.4 GHz with 99\% confidence. If all pulsars emit from opposite poles of a dipolar magnetic field with comparable brightness, we might expect to see evidence of an interpulse arising in PSR J1141$-$6545, unless the emission is patchy.Comment: Accepted for publication in Astrophysical Journal Letter