Hydrodynamic View of Wave-Packet Interference: Quantum Caves

Wave-packet interference is investigated within the complex quantum Hamilton-Jacobi formalism using a hydrodynamic description. Quantum interference leads to the formation of the topological structure of quantum caves in space-time Argand plots. These caves consist of the vortical and stagnation tubes originating from the isosurfaces of the amplitude of the wave function and its first derivative. Complex quantum trajectories display counterclockwise helical wrapping around the stagnation tubes and hyperbolic deflection near the vortical tubes. The string of alternating stagnation and vortical tubes is sufficient to generate divergent trajectories. Moreover, the average wrapping time for trajectories and the rotational rate of the nodal line in the complex plane can be used to define the lifetime for interference features.Comment: 4 pages, 3 figures (major revisions with respect to the previous version have been carried out

A causal look into the quantum Talbot effect

A well-known phenomenon in both optics and quantum mechanics is the so-called Talbot effect. This near field interference effect arises when infinitely periodic diffracting structures or gratings are illuminated by highly coherent light or particle beams. Typical diffraction patterns known as quantum carpets are then observed. Here the authors provide an insightful picture of this nonlocal phenomenon as well as its classical limit in terms of Bohmian mechanics, also showing the causal reasons and conditions that explain its appearance. As an illustration, theoretical results obtained from diffraction of thermal He atoms by both N-slit arrays and weak corrugated surfaces are analyzed and discussed. Moreover, the authors also explain in terms of what they call the Talbot-Beeby effect how realistic interaction potentials induce shifts and distortions in the corresponding quantum carpets.Comment: 12 pages, 6 figure

Reference curves for a fitness battery developed for children ages 5-12 years in England

Purpose: Reference curves have already been created for a variety of different physical testing batteries across a number of countries. Due to results differing between countries for the same sex and age, it is important that reference curves are created specific for each country. Therefore, the aim of this study was to provide reference curves for five different fitness tests that assess the core components of health related fitness within children in England. Method: Following institutional ethics approval, parental informed consent and child assent was obtained for a total of 39,199 children aged between 5 and 12 years completed tests for explosive power, agility, hand eye coordination, lower body strength and upper body strength. To calculate reference values Generalised Additive Models for Location, Scale and Shape (GAMLSS) were used. Results: Reference curves and centiles show differences in performance levels of the fitness tests between sex and age groups. These reference curves and centiles provide age and sex comparisons to enable progress monitoring of children's physical fitness competence within England and comparisons to other countries. Conclusion: Girls are outperformed from a young age group and both upper and lower body strength decreases are seen at ages nine and ten. In physical activity and health related fitness interventions, both girls and boys in Key stage two should be targeted to maintain progression and lessen the gender divide

Reference curves for a fitness battery developed for children ages 5-12 years in England

Purpose: Reference curves have already been created for a variety of different physical testing batteries across a number of countries. Due to results differing between countries for the same sex and age, it is important that reference curves are created specific for each country. Therefore, the aim of this study was to provide reference curves for five different fitness tests that assess the core components of health related fitness within children in England. Method: Following institutional ethics approval, parental informed consent and child assent was obtained for a total of 39,199 children aged between 5 and 12 years completed tests for explosive power, agility, hand eye coordination, lower body strength and upper body strength. To calculate reference values Generalised Additive Models for Location, Scale and Shape (GAMLSS) were used. Results: Reference curves and centiles show differences in performance levels of the fitness tests between sex and age groups. These reference curves and centiles provide age and sex comparisons to enable progress monitoring of children's physical fitness competence within England and comparisons to other countries. Conclusion: Girls are outperformed from a young age group and both upper and lower body strength decreases are seen at ages nine and ten. In physical activity and health related fitness interventions, both girls and boys in Key stage two should be targeted to maintain progression and lessen the gender divide

Field Trials with Zinc on Corn

Zinc deficiency in corn has been found in isolated instances in Kentucky during the past few years. Usually the deficiency is found in fields having a high pH or in high-phosphate soils with somewhat lower pH values. At present zinc deficiency in Kentucky soils does not appear widespread enough to justify recommending its application except where known deficiencies exist

How Observations of Circumstellar Disk Asymmetries Can Reveal Hidden Planets: Pericenter Glow and its Application to the HR 4796 Disk

Recent images of the disks of dust around the young stars HR 4796A and Fomalhaut show, in each case, a double-lobed feature that may be asymmetric (one lobe may be brighter than the other). A symmetric double-lobed structure is that expected from a disk of dust with a central hole that is observed nearly edge-on (i.e., close to the plane of the disk). This paper shows how the gravitational influence of a second body in the system with an eccentric orbit would cause a brightness asymmetry in such a disk by imposing a "forced eccentricity" on the orbits of the constituent dust particles, thus shifting the center of symmetry of the disk away from the star and causing the dust near the forced pericenter of the perturbed disk to glow. Dynamic modeling of the HR 4796 disk shows that its 5% brightness asymmetry could be the result of a forced eccentricity as small as 0.02 imposed on the disk by either the binary companion HR 4796B, or by an unseen planet close to the inner edge of the disk. Since it is likely that a forced eccentricity of 0.01 or higher would be imposed on a disk in a system in which there are planets, but no binary companion, the corresponding asymmetry in the disk's structure could serve as a sensitive indicator of these planets that might otherwise remain undetected.Comment: 61 pages, 10 figures, accepted for publication in the Astrophysical Journal (scheduled for January 10, 2000

Multi-Epoch Observations of HD69830: High Resolution Spectroscopy and Limits to Variability

The main-sequence solar-type star HD69830 has an unusually large amount of dusty debris orbiting close to three planets found via the radial velocity technique. In order to explore the dynamical interaction between the dust and planets, we have performed multi-epoch photometry and spectroscopy of the system over several orbits of the outer dust. We find no evidence for changes in either the dust amount or its composition, with upper limits of 5-7% (1 $\sigma$ per spectral element) on the variability of the {\it dust spectrum} over 1 year, 3.3% (1 $\sigma$) on the broad-band disk emission over 4 years, and 33% (1 $\sigma$) on the broad-band disk emission over 24 years. Detailed modeling of the spectrum of the emitting dust indicates that the dust is located outside of the orbits of the three planets and has a composition similar to main-belt, C-type asteroids asteroids in our solar system. Additionally, we find no evidence for a wide variety of gas species associated with the dust. Our new higher SNR spectra do not confirm our previously claimed detection of H$_2$O ice leading to a firm conclusion that the debris can be associated with the break-up of one or more C-type asteroids formed in the dry, inner regions of the protoplanetary disk of the HD69830 system. The modeling of the spectral energy distribution and high spatial resolution observations in the mid-infrared are consistent with a $\sim$ 1 AU location for the emitting material

Monte Carlo Generation of Bohmian Trajectories

We report on a Monte Carlo method that generates one-dimensional trajectories for Bohm's formulation of quantum mechanics that doesn't involve differentiation or integration of any equations of motion. At each time, t=n\delta t (n=1,2,3,...), N particle positions are randomly sampled from the quantum probability density. Trajectories are built from the sorted N sampled positions at each time. These trajectories become the exact Bohm solutions in the limits N->\infty and \delta t -> 0. Higher dimensional problems can be solved by this method for separable wave functions. Several examples are given, including the two-slit experiment.Comment: 10 pages, 6 figure

Reconciling Semiclassical and Bohmian Mechanics: II. Scattering states for discontinuous potentials

In a previous paper [J. Chem. Phys. 121 4501 (2004)] a unique bipolar decomposition, Psi = Psi1 + Psi2 was presented for stationary bound states Psi of the one-dimensional Schroedinger equation, such that the components Psi1 and Psi2 approach their semiclassical WKB analogs in the large action limit. Moreover, by applying the Madelung-Bohm ansatz to the components rather than to Psi itself, the resultant bipolar Bohmian mechanical formulation satisfies the correspondence principle. As a result, the bipolar quantum trajectories are classical-like and well-behaved, even when Psi has many nodes, or is wildly oscillatory. In this paper, the previous decomposition scheme is modified in order to achieve the same desirable properties for stationary scattering states. Discontinuous potential systems are considered (hard wall, step, square barrier/well), for which the bipolar quantum potential is found to be zero everywhere, except at the discontinuities. This approach leads to an exact numerical method for computing stationary scattering states of any desired boundary conditions, and reflection and transmission probabilities. The continuous potential case will be considered in a future publication.Comment: 18 pages, 8 figure

Young "Dipper" Stars in Upper Sco and ρ\rho Oph Observed by K2

We present ten young ($\lesssim$10 Myr) late-K and M dwarf stars observed in K2 Campaign 2 that host protoplanetary disks and exhibit quasi-periodic or aperiodic dimming events. Their optical light curves show $\sim$10-20 dips in flux over the 80-day observing campaign with durations of $\sim$0.5-2 days and depths of up to $\sim$40%. These stars are all members of the $\rho$ Ophiuchus ($\sim$1 Myr) or Upper Scorpius ($\sim$10 Myr) star-forming regions. To investigate the nature of these "dippers" we obtained: optical and near-infrared spectra to determine stellar properties and identify accretion signatures; adaptive optics imaging to search for close companions that could cause optical variations and/or influence disk evolution; and millimeter-wavelength observations to constrain disk dust and gas masses. The spectra reveal Li I absorption and H$\alpha$ emission consistent with stellar youth (<50 Myr), but also accretion rates spanning those of classical and weak-line T Tauri stars. Infrared excesses are consistent with protoplanetary disks extending to within $\sim$10 stellar radii in most cases; however, the sub-mm observations imply disk masses that are an order of magnitude below those of typical protoplanetary disks. We find a positive correlation between dip depth and WISE-2 excess, which we interpret as evidence that the dipper phenomenon is related to occulting structures in the inner disk, although this is difficult to reconcile with the weakly accreting aperiodic dippers. We consider three mechanisms to explain the dipper phenomenon: inner disk warps near the co-rotation radius related to accretion; vortices at the inner disk edge produced by the Rossby Wave Instability; and clumps of circumstellar material related to planetesimal formation.Comment: Accepted to ApJ, 19 pages, 10 figure