Uniform analytic approximation of Wigner rotation matrices

We derive the leading asymptotic approximation, for low angle {\theta}, of the Wigner rotation matrix elements $d^j_{m_1m_2}(\theta)$, uniform in $j,m_1$ and $m_2$. The result is in terms of a Bessel function of integer order. We numerically investigate the error for a variety of cases and find that the approximation can be useful over a significant range of angles. This approximation has application in the partial wave analysis of wavepacket scattering.Comment: 8 pages, 5 figure

Prediction of deviations from the Rutherford formula for low-energy Coulomb scattering of wavepackets

We calculate the nonrelativistic scattering of a wavepacket from a Coulomb potential and find deviations from the Rutherford formula in all cases. These generally occur only at low scattering angles, where they would be obscured by the part of the incident beam that emerges essentially unscattered. For a model experiment, the scattering of helium nuclei from a thin gold foil, we find the deviation region is magnified for low incident energies (in the keV range), so that a large shadow zone of low probability around the forward direction is expected to be measurable. From a theoretical perspective, the use of wavepackets makes partial wave analysis applicable to this infinite-range potential. It allows us to calculate the everywhere finite probability for a wavepacket to wavepacket transition and to relate this to the differential cross section. Time delays and advancements in the detection probabilities can be calculated. We investigate the optical theorem as applied to this special case.Comment: 21 pages, 8 figures. This version contains clarifications and additional results compared to the previous version. The paper has been accepted for publication in J.Phys.

Resistance decay in individuals after antibiotic exposure in primary care: A systematic review and meta-analysis

Abstract Background Antibiotic resistance is an urgent global problem, but reversibility is poorly understood. We examined the development and decay of bacterial resistance in community patients after antibiotic use. Methods This was a systematic review and meta-analysis. PubMed, EMBASE and CENTRAL (from inception to May 2017) were searched, with forward and backward citation searches of the identified studies. We contacted authors whose data were unclear, and of abstract-only reports, for further information. We considered controlled or times-series studies of patients in the community who were given antibiotics and where the subsequent prevalence of resistant bacteria was measured. Two authors extracted risk of bias and data. The meta-analysis used a fixed-effects model. Results Of 24,492 articles screened, five controlled and 20 time-series studies (total 16,353 children and 1461 adults) were eligible. Resistance in Streptococcus pneumoniae initially increased fourfold after penicillin-class antibiotic exposure [odds ratio (OR) 4.2, 95% confidence interval (CI) 3.5–5.4], but this fell after 1 month (OR 1.7, 95% CI 1.3–2.1). After cephalosporin-class antibiotics, resistance increased (OR 2.2, 95%CI 1.7-2.9); and fell to (OR 1.6, 95% CI 1.2-2.3) at 1 month. After macrolide-class antibiotics, resistance increased (OR 3.8, 95% CI 1.9–7.6) and persisted for 1 month (OR 5.2, 95% CI 2.6–10.3) and 3 months (OR 8.1, 95% CI 4.6–14.2, from controlled studies and OR 2.3, 95% CI 0.6–9.4, from time-series studies). Resistance in Haemophilus influenzae after penicillins was not significantly increased (OR 1.3, 95% CI 0.9–1.9) initially but was at 1 month (OR 3.4, 95% CI 1.5–7.6), falling after 3 months (OR 1.0, 95% CI 0.5–2.2). Data were sparse for cephalosporins and macrolides. Resistance in Enterobacter increased post-exposure (OR 3.2, 95% CI 0.9–10.8, from controlled studies and OR 7.1, 95% CI 4.2–12, from time-series studies], but was lower after 1 month (OR 1.8, 95% CI 0.9–3.6). Conclusions Resistance generally increased soon after antibiotic use. For some antibiotic classes and bacteria, it partially diminished after 1 and 3 months, but longer-term data are lacking and urgently needed. Trial registration PROSPERO CRD42015025499

Hybrid phase-space simulation method for interacting Bose fields

We introduce an approximate phase-space technique to simulate the quantum dynamics of interacting bosons. With the future goal of treating Bose-Einstein condensate systems, the method is designed for systems with a natural separation into highly occupied (condensed) modes and lightly occupied modes. The method self-consistently uses the Wigner representation to treat highly occupied modes and the positive-P representation for lightly occupied modes. In this method, truncation of higher-derivative terms from the Fokker-Planck equation is usually necessary. However, at least in the cases investigated here, the resulting systematic error, over a finite time, vanishes in the limit of large Wigner occupation numbers. We tested the method on a system of two interacting anharmonic oscillators, with high and low occupations, respectively. The Hybrid method successfully predicted atomic quadratures to a useful simulation time 60 times longer than that of the positive-P method. The truncated Wigner method also performed well in this test. For the prediction of the correlation in a quantum nondemolition measurement scheme, for this same system, the Hybrid method gave excellent agreement with the exact result, while the truncated Wigner method showed a large systematic error.Comment: 13 pages; 6 figures; references added; figures correcte