Discrete Accidental Symmetry for a Particle in a Constant Magnetic Field on a Torus

A classical particle in a constant magnetic field undergoes cyclotron motion on a circular orbit. At the quantum level, the fact that all classical orbits are closed gives rise to degeneracies in the spectrum. It is well-known that the spectrum of a charged particle in a constant magnetic field consists of infinitely degenerate Landau levels. Just as for the $1/r$ and $r^2$ potentials, one thus expects some hidden accidental symmetry, in this case with infinite-dimensional representations. Indeed, the position of the center of the cyclotron circle plays the role of a Runge-Lenz vector. After identifying the corresponding accidental symmetry algebra, we re-analyze the system in a finite periodic volume. Interestingly, similar to the quantum mechanical breaking of CP invariance due to the $\theta$-vacuum angle in non-Abelian gauge theories, quantum effects due to two self-adjoint extension parameters $\theta_x$ and $\theta_y$ explicitly break the continuous translation invariance of the classical theory. This reduces the symmetry to a discrete magnetic translation group and leads to finite degeneracy. Similar to a particle moving on a cone, a particle in a constant magnetic field shows a very peculiar realization of accidental symmetry in quantum mechanics.Comment: 25 pages, 2 figure

Combined CI+MBPT calculations of energy levels and transition amplitudes in Be, Mg, Ca, and Sr

Configuration interaction (CI) calculations in atoms with two valence electrons, carried out in the V(N-2) Hartree-Fock potential of the core, are corrected for core-valence interactions using many-body perturbation theory (MBPT). Two variants of the mixed CI+MBPT theory are described and applied to obtain energy levels and transition amplitudes for Be, Mg, Ca, and Sr

Feasibility of undertaking off-site infant eye-tracking assessments of neuro-cognitive functioning in early-intervention centres

Recent work suggests that differences in functional brain development are already identifiable in 6- to 9-month-old infants from low socio-economic status (SES) backgrounds. Investigation of early SES-related differences in neuro-cognitive functioning requires the recruitment of large and diverse samples of infants, yet it is often difficult to persuade low-SES parents to come to a university setting. One solution is to recruit infants through early intervention children’s centres (CCs). These are often located in areas of high relative deprivation to support young children. Given the increasing portability of eye-tracking equipment, assessment of large clusters of infants could be undertaken in centres by suitably trained early intervention staff. Here we report on a study involving 174 infants and their parents, carried out in partnership with CCs, exploring the feasibility of this approach, We report the processes of setting up the project and participant recruitment. We report the diversity of sample obtained on the engagement of CC staff in training and the process of assessment itself. We report the quality of the data obtained, and the levels of engagement of parents, and infants. We conclude that this approach has great potential for recruiting large and diverse samples worldwide, provides sufficiently reliable data, and is engaging to staff, parents and infants

Visual motherese? Signal-to-noise ratios in toddler-directed television

Younger brains are noisier information processing systems; this means that information for younger individuals has to allow clearer differentiation between those aspects that are required for the processing task in hand (the ‘signal’) and those that are not (the ‘noise’). We compared toddler-directed and adult-directed TV programmes (TotTV/ATV). We examined how low-level visual features (that previous research has suggested influence gaze allocation) relate to semantic information, namely the location of the character speaking in each frame. We show that this relationship differs between TotTV and ATV. First, we conducted Receiver Operator Characteristics analyses and found that feature congestion predicted speaking character location in TotTV but not ATV. Second, we used multiple analytical strategies to show that luminance differentials (flicker) predict face location more strongly in TotTV than ATV. Our results suggest that TotTV designers have intuited techniques for controlling toddler attention using low-level visual cues. The implications of these findings for structuring childhood learning experiences away from a screen are discussed

Space Vehicle Terrestrial Environment Design Requirements Guidelines

The terrestrial environment is an important driver of space vehicle structural, control, and thermal system design. NASA is currently in the process of producing an update to an earlier Terrestrial Environment Guidelines for Aerospace Vehicle Design and Development Handbook. This paper addresses the contents of this updated handbook, with special emphasis on new material being included in the areas of atmospheric thermodynamic models, wind dynamics, atmospheric composition, atmospheric electricity, cloud phenomena, atmospheric extremes, and sea state. In addition, the respective engineering design elements are discussed relative to terrestrial environment inputs that require consideration. Specific lessons learned that have contributed to the advancements made in the application and awareness of terrestrial environment inputs for aerospace engineering applications are presented

Trapping of Projectiles in Fixed Scatterer Calculations

We study multiple scattering off nuclei in the closure approximation. Instead of reducing the dynamics to one particle potential scattering, the scattering amplitude for fixed target configurations is averaged over the target groundstate density via stochastic integration. At low energies a strong coupling limit is found which can not be obtained in a first order optical potential approximation. As its physical explanation, we propose it to be caused by trapping of the projectile. We analyse this phenomenon in mean field and random potential approximations. (PACS: 24.10.-i)Comment: 15 page

Efficiency of scanning and attention to faces in infancy independently predict language development in a multiethnic and bilingual sample of 2-year-olds

Efficient visual exploration in infancy is essential for cognitive and language development. It allows infants to participate in social interactions by attending to faces and learning about objects of interest. Visual scanning of scenes depends on a number of factors and early differences in efficiency are likely contributing to differences in learning and language development during subsequent years. Predicting language development in diverse samples is particularly challenging, as additional multiple sources of variability affect infant performance. In this study we tested how the complexity of visual scanning in the presence or absence of a face at 6-7 months of age is related to language development at 2 years of age in a multi-ethnic and predominantly bilingual sample from diverse socio-economic backgrounds. We used Recurrence Quantification Analysis to measure the temporal and spatial distribution of fixations recurring in the same area of a visual scene. We found that in the absence of a face the temporal distribution of re-fixations on selected objects of interest (but not all) significantly predicted both receptive and expressive language scores, explaining 16 - 20% of the variance. Also, lower rate of re-fixations recurring in the presence of a face predicted higher receptive language scores, suggesting larger vocabulary in infants that effectively disengage from faces. Altogether, our results suggest that dynamic measures, which quantify the complexity of visual scanning can reliably and robustly predict language development in highly diverse samples. They suggest that selective attending to objects predicts language independently of attention to faces. As eye-tracking and language assessments were carried out in early intervention centres, our study demonstrates the utility of mobile eye-tracking setups for early detection of risk in attention and language development