Analytic results for Gaussian wave packets in four model systems: II. Autocorrelation functions

The autocorrelation function, A(t), measures the overlap (in Hilbert space) of a time-dependent quantum mechanical wave function, psi(x,t), with its initial value, psi(x,0). It finds extensive use in the theoretical analysis and experimental measurement of such phenomena as quantum wave packet revivals. We evaluate explicit expressions for the autocorrelation function for time-dependent Gaussian solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium (the so-called `inverted' oscillator.) We emphasize the importance of momentum-space methods where such calculations are often more straightforwardly realized, as well as stressing their role in providing complementary information to results obtained using position-space wavefunctions.Comment: 18 pages, RevTeX, to appear in Found. Phys. Lett, Vol. 17, Dec. 200

Analytic results for Gaussian wave packets in four model systems: I. Visualization of the kinetic energy

Using Gaussian wave packet solutions, we examine how the kinetic energy is distributed in time-dependent solutions of the Schrodinger equation corresponding to the cases of a free particle, a particle undergoing uniform acceleration, a particle in a harmonic oscillator potential, and a system corresponding to an unstable equilibrium. We find, for specific choices of initial parameters, that as much as 90% of the kinetic energy can be localized (at least conceptually) in the `front half' of such Gaussian wave packets, and we visualize these effects.Comment: 22 pages, RevTeX, four .eps figures, to appear in Found. Phys. Lett. Vol. 17, Dec. 200

IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) in primary care: study protocol for a cluster randomised controlled implementation trial

BACKGROUND: Asthma is a common long-term condition and major public health problem. Supported self-management for asthma that includes a written personalised asthma action plan, supported by regular professional review, reduces unscheduled consultations and improves asthma outcomes and quality of life. However, despite unequivocal inter/national guideline recommendations, supported self-management is poorly implemented in practice. The IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) implementation strategy has been developed to address this challenge. The aim of this implementation trial is to determine whether facilitated delivery of the IMP2ART strategy increases the provision of asthma action plans and reduces unscheduled care in the context of routine UK primary care. METHODS: IMP2ART is a parallel group, cluster randomised controlled hybrid II implementation trial. One hundred forty-four general practices will be randomly assigned to either the IMP2ART implementation strategy or control group. Following a facilitation workshop, implementation group practices will receive organisational resources to help them prioritise supported self-management (including audit and feedback; an IMP2ART asthma review template), training for professionals and resources to support patients to self-manage their asthma. The control group will continue with usual asthma care. The primary clinical outcome is the between-group difference in unscheduled care in the second year after randomisation (i.e. between 12 and 24 months post-randomisation) assessed from routine data. Additionally, a primary implementation outcome of asthma action plan ownership at 12 months will be assessed by questionnaire to a random sub-group of people with asthma. Secondary outcomes include the number of asthma reviews conducted, prescribing outcomes (reliever medication and oral steroids), asthma symptom control, patients' confidence in self-management and professional support and resource use. A health economic analysis will assess cost-effectiveness, and a mixed methods process evaluation will explore implementation, fidelity and adaptation. DISCUSSION: The evidence for supported asthma self-management is overwhelming. This study will add to the literature regarding strategies that can effectively implement supported self-management in primary care to reduce unscheduled consultations and improve asthma outcomes and quality of life. TRIAL REGISTRATION: ISRCTN15448074. Registered on 2 December 2019

Eikonal analysis of Coulomb distortion in quasi-elastic electron scattering

An eikonal expansion is used to provide systematic corrections to the eikonal approximation through order $1/k^2$, where $k$ is the wave number. Electron wave functions are obtained for the Dirac equation with a Coulomb potential. They are used to investigate distorted-wave matrix elements for quasi-elastic electron scattering from a nucleus. A form of effective-momentum approximation is obtained using trajectory-dependent eikonal phases and focusing factors. Fixing the Coulomb distortion effects at the center of the nucleus, the often-used ema approximation is recovered. Comparisons of these approximations are made with full calculations using the electron eikonal wave functions. The ema results are found to agree well with the full calculations.Comment: 12 pages, 6 Postscript figure

Weak localization of light by cold atoms: the impact of quantum internal structure

Since the work of Anderson on localization, interference effects for the propagation of a wave in the presence of disorder have been extensively studied, as exemplified in coherent backscattering (CBS) of light. In the multiple scattering of light by a disordered sample of thermal atoms, interference effects are usually washed out by the fast atomic motion. This is no longer true for cold atoms where CBS has recently been observed. However, the internal structure of the atoms strongly influences the interference properties. In this paper, we consider light scattering by an atomic dipole transition with arbitrary degeneracy and study its impact on coherent backscattering. We show that the interference contrast is strongly reduced. Assuming a uniform statistical distribution over internal degrees of freedom, we compute analytically the single and double scattering contributions to the intensity in the weak localization regime. The so-called ladder and crossed diagrams are generalized to the case of atoms and permit to calculate enhancement factors and backscattering intensity profiles for polarized light and any closed atomic dipole transition.Comment: 22 pages Revtex, 9 figures, to appear in PR

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced in $ep$ interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function of \xpom, the momentum fraction lost by the proton, of $\beta$, the momentum fraction of the struck quark with respect to \xpom, and of $Q^2$. The \xpom dependence is consistent with the form \xpoma where $a~=~1.30~\pm~0.08~(stat)~^{+~0.08}_{-~0.14}~(sys)$ in all bins of $\beta$ and $Q^2$. In the measured $Q^2$ range, the diffractive structure function approximately scales with $Q^2$ at fixed $\beta$. In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.Comment: 36 pages, latex, 11 figures appended as uuencoded fil

Measurement of inclusive D*+- and associated dijet cross sections in photoproduction at HERA

Inclusive photoproduction of D*+- mesons has been measured for photon-proton centre-of-mass energies in the range 130 < W < 280 GeV and a photon virtuality Q^2 < 1 GeV^2. The data sample used corresponds to an integrated luminosity of 37 pb^-1. Total and differential cross sections as functions of the D* transverse momentum and pseudorapidity are presented in restricted kinematical regions and the data are compared with next-to-leading order (NLO) perturbative QCD calculations using the "massive charm" and "massless charm" schemes. The measured cross sections are generally above the NLO calculations, in particular in the forward (proton) direction. The large data sample also allows the study of dijet production associated with charm. A significant resolved as well as a direct photon component contribute to the cross section. Leading order QCD Monte Carlo calculations indicate that the resolved contribution arises from a significant charm component in the photon. A massive charm NLO parton level calculation yields lower cross sections compared to the measured results in a kinematic region where the resolved photon contribution is significant.Comment: 32 pages including 6 figure

IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) in primary care: study protocol for a cluster randomised controlled implementation trial.

BACKGROUND: Asthma is a common long-term condition and major public health problem. Supported self-management for asthma that includes a written personalised asthma action plan, supported by regular professional review, reduces unscheduled consultations and improves asthma outcomes and quality of life. However, despite unequivocal inter/national guideline recommendations, supported self-management is poorly implemented in practice. The IMPlementing IMProved Asthma self-management as RouTine (IMP2ART) implementation strategy has been developed to address this challenge. The aim of this implementation trial is to determine whether facilitated delivery of the IMP2ART strategy increases the provision of asthma action plans and reduces unscheduled care in the context of routine UK primary care. METHODS: IMP2ART is a parallel group, cluster randomised controlled hybrid II implementation trial. One hundred forty-four general practices will be randomly assigned to either the IMP2ART implementation strategy or control group. Following a facilitation workshop, implementation group practices will receive organisational resources to help them prioritise supported self-management (including audit and feedback; an IMP2ART asthma review template), training for professionals and resources to support patients to self-manage their asthma. The control group will continue with usual asthma care. The primary clinical outcome is the between-group difference in unscheduled care in the second year after randomisation (i.e. between 12 and 24 months post-randomisation) assessed from routine data. Additionally, a primary implementation outcome of asthma action plan ownership at 12 months will be assessed by questionnaire to a random sub-group of people with asthma. Secondary outcomes include the number of asthma reviews conducted, prescribing outcomes (reliever medication and oral steroids), asthma symptom control, patients' confidence in self-management and professional support and resource use. A health economic analysis will assess cost-effectiveness, and a mixed methods process evaluation will explore implementation, fidelity and adaptation. DISCUSSION: The evidence for supported asthma self-management is overwhelming. This study will add to the literature regarding strategies that can effectively implement supported self-management in primary care to reduce unscheduled consultations and improve asthma outcomes and quality of life. TRIAL REGISTRATION: ISRCTN15448074. Registered on 2 December 2019

Measurement of Jet Shapes in Photoproduction at HERA

The shape of jets produced in quasi-real photon-proton collisions at centre-of-mass energies in the range $134-277$ GeV has been measured using the hadronic energy flow. The measurement was done with the ZEUS detector at HERA. Jets are identified using a cone algorithm in the $\eta - \phi$ plane with a cone radius of one unit. Measured jet shapes both in inclusive jet and dijet production with transverse energies $E^{jet}_T>14$ GeV are presented. The jet shape broadens as the jet pseudorapidity ($\eta^{jet}$) increases and narrows as $E^{jet}_T$ increases. In dijet photoproduction, the jet shapes have been measured separately for samples dominated by resolved and by direct processes. Leading-logarithm parton-shower Monte Carlo calculations of resolved and direct processes describe well the measured jet shapes except for the inclusive production of jets with high $\eta^{jet}$ and low $E^{jet}_T$. The observed broadening of the jet shape as $\eta^{jet}$ increases is consistent with the predicted increase in the fraction of final state gluon jets.Comment: 29 pages including 9 figure