Energy spectra of two interacting fermions with spin-orbit coupling in a harmonic trap

We explore the two-body spectra of spin-$1/2$ fermions in isotropic harmonic traps with external spin-orbit potentials and short range two-body interactions. Using a truncated basis of total angular momentum eigenstates, non-perturbative results are presented for experimentally realistic forms of the spin-orbit coupling: a pure Rashba coupling, Rashba and Dresselhaus couplings in equal parts, and a Weyl-type coupling. The technique is easily adapted to bosonic systems and other forms of spin-orbit coupling.Comment: 12 pages, 9 figure

Water Ice in 2060 Chiron and its Implications for Centaurs and Kuiper Belt Objects

We report the detection of water ice in the Centaur 2060 Chiron, based on near-infrared spectra (1.0 - 2.5 micron) taken with the 3.8-meter United Kingdom Infrared Telescope (UKIRT) and the 10-meter Keck Telescope. The appearance of this ice is correlated with the recent decline in Chiron's cometary activity: the decrease in the coma cross-section allows previously hidden solid-state surface features to be seen. We predict that water ice is ubiquitous among Centaurs and Kuiper Belt objects, but its surface coverage varies from object to object, and thus determines its detectability and the occurrence of cometary activity.Comment: 18 pages, 3 figures, accepted by ApJ Letter

Population of the Scattered Kuiper Belt

We present the discovery of three new Scattered Kuiper Belt Objects (SKBOs) from a wide-field survey of the ecliptic. This continuing survey has to date covered 20.2 square degrees to a limiting red magnitude of 23.6. We combine the data from this new survey with an existing survey conducted at the University of Hawaii 2.2m telescope to constrain the number and mass of the SKBOs. The SKBOs are characterized by large eccentricities, perihelia near 35 AU, and semi-major axes > 50 AU. Using a maximum-likelihood model, we estimate the total number of SKBOs larger than 100 km in diameter to be N = 3.1 (+1.9/-1.3) x 10^4 (1 sigma) and the total mass of SKBOs to be about 0.05 Earth masses, demonstrating that the SKBOs are similar in number and mass to the Kuiper Belt inside 50 AU.Comment: 15 pages, 3 figure

Effective Interactions for the Three-Body Problem

The three-body energy-dependent effective interaction given by the Bloch-Horowitz (BH) equation is evaluated for various shell-model oscillator spaces. The results are applied to the test case of the three-body problem (triton and He3), where it is shown that the interaction reproduces the exact binding energy, regardless of the parameterization (number of oscillator quanta or value of the oscillator parameter b) of the low-energy included space. We demonstrate a non-perturbative technique for summing the excluded-space three-body ladder diagrams, but also show that accurate results can be obtained perturbatively by iterating the two-body ladders. We examine the evolution of the effective two-body and induced three-body terms as b and the size of the included space Lambda are varied, including the case of a single included shell, Lambda hw=0 hw. For typical ranges of b, the induced effective three-body interaction, essential for giving the exact three-body binding, is found to contribute ~10% to the binding energy.Comment: 19 pages, 9 figures, submitted to PR

Effect of Stimulus Orientation on Visual Function in Children with Refractive Amblyopia.

Purpose: We investigated and characterized the patterns of meridional anisotropies in newly diagnosed refractive amblyopes using pattern onset–offset visual evoked potentials (POVEPs) and psychophysical grating acuity (GA). Methods: Twenty-five refractive amblyopes were recruited and compared with non-amblyopic controls from our previous study. Monocular POVEPs were recorded in response to sinewave 4 cycles per degree (cpd) grating stimuli oriented along each individual participants' principal astigmatic meridians, which were approximately horizontal (meridian 1) and vertical (meridian 2). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed along the same meridians using a two-alternative non-forced-choice technique. The C3 amplitudes and peak latencies of the POVEPs and GAs were compared across meridians for both groups (refractive amblyopes and controls) using linear mixed models (monocular) and ANOVA (binocular), and post hoc analysis was conducted to determine if meridional anisotropies in this cohort of amblyopes were related to low (≤1.50 diopters [D]), moderate (1.75–2.75 D) and high (≥3.00 D) astigmatism. Results: In the newly diagnosed refractive amblyopes, there were no significant meridional anisotropies across all outcome measures, but the post hoc analysis demonstrated that C3 amplitude was significantly higher in those with low (P = 0.02) and moderate (P = 0.004) astigmatism compared to those with high astigmatism. Refractive amblyopes had poorer GA and C3 amplitudes compared to controls by approximately two lines on the logMAR chart (monocular: P = 0.013; binocular: P = 0.014) and approximately 6 µV (monocular: P = 0.009; binocular: P = 0.027), respectively. Conclusions: Deleterious effects of high astigmatism was evident in newly diagnosed refractive amblyopes, but the neural deficits do not seem to be orientation-specific for the stimulus parameters investigated

Electrophysiological and Psychophysical Studies of Meridional Anisotropies in Children With and Without Astigmatism.

Purpose: We investigated the pattern of meridional anisotropies, if any, for pattern onset-offset visual evoked potential (POVEPs) responses and psychophysical grating acuity (GA) in children with normal letter visual acuity (20/20 or better). Methods: A total of 29 children (aged 3-9 years), nine of whom were astigmatic (AS), were recruited. Orientation-specific monocular POVEPs were recorded in response to sinewave grating stimuli oriented along the subjects' principal AS meridians. Horizontal and vertical gratings were designated Meridians 1 and 2, respectively, for nonastigmatic patients (Non-AS). Binocular POVEPs in response to the same stimuli, but oriented at 45°, 90°, 135°, and 180°, were recorded. Psychophysical GAs were assessed monocularly and binocularly along the same meridians using the same stimuli by a 2-alternative-forced-choice staircase technique. The C3 amplitudes and peak latencies of the POVEP and GAs were compared across meridians using linear mixed models (monocular) and ANOVA (binocular). Results: There were significant meridional anisotropies in monocular C3 amplitudes regardless of astigmatism status (P = 0.001): Meridian 2 (mean ± SE Non-AS, 30.13 ± 2.07 μV; AS, 26.53 ± 2.98 μV) was significantly higher than Meridian 1 (Non-AS, 26.14 ± 1.87 μV; AS, 21.68 ± 2.73 μV; P = 0.019), but no meridional anisotropies were found for GA or C3 latency. Binocular C3 amplitude in response to horizontally oriented stimuli (180°, 29.71 ± 3.06 μV) was significantly lower than the oblique (45°, 36.62 ± 3 .05 μV; P = 0.03 and 135°, 35.95 ± 2.92 μV; P = 0.04) and vertical (90°, 37.82 ± 3.65 μV; P = 0.02) meridians, and binocular C3 latency was significantly shorter in response to vertical than oblique gratings (P ≤ 0.001). Conclusions: Meridional anisotropy was observed in children with normal vision. The findings suggest that horizontal gratings result in a small, but significantly lower POVEP amplitude than for vertical and oblique gratings

Thermoelectric properties of BiOCu1-xMxSe (M = Cd and Zn)

Doping of BiOCuSe at the copper site with divalent cadmium and zinc cations has been investigated. Analysis of the powder X-ray diffraction data indicates that the ZrCuSiAs structure of BiOCuSe is retained up to substitution levels of 10 and 5 at.% for Cd2+ and Zn2+, respectively. Substitution of monovalent Cu+ with divalent Cd2+ or Zn2+ leads to an increase in the magnitude of the electrical resistivity and the Seebeck coefficient. All synthesized materials behave as p-type semiconductors

Multi-Pion States in Lattice QCD and the Charged-Pion Condensate

The ground-state energies of systems containing up to twelve $\pi^+$'s in a spatial volume V ~ (2.5 fm)^3 are computed in dynamical, mixed-action lattice QCD at a lattice spacing of ~ 0.125 fm for four different values of the light quark masses. Clean signals are seen for each ground state, allowing for a precise extraction of both the $\pi^+\pi^+$ scattering length and $\pi^+\pi^+\pi^+$-interaction from a correlated analysis of systems containing different numbers of $\pi^+$'s. This extraction of the $\pi^+\pi^+$ scattering length is consistent with than that from the $\pi^+\pi^+$-system alone. The large number of systems studied here significantly strengthens the arguments presented in our earlier work and unambiguously demonstrates the presence of a low energy $\pi^+\pi^+\pi^+$-interaction. The equation of state of a $\pi^+$ gas is investigated using our numerical results and the density dependence of the isospin chemical potential for these systems agrees well with the theoretical expectations of leading order chiral perturbation theory. The chemical potential is found to receive a substantial contribution from the $\pi^+\pi^+\pi^+$-interaction at the lighter pion masses. An important technical aspect of this work is the demonstration of the necessity of performing propagator contractions in greater than double precision to extract the correct results.Comment: 38 pages, 20 figure