Spin dynamics and structure formation in a spin-1 condensate in a magnetic field

We study the dynamics of a trapped spin-1 condensate in a magnetic field. First, we analyze the homogeneous system, for which the dynamics can be understood in terms of orbits in phase space. We analytically solve for the dynamical evolution of the populations of the various Zeeman components of the homogeneous system. This result is then applied via a local-density approximation to trapped quasi-one-dimensional condensates. Our analysis of the trapped system in a magnetic field shows that both the mean-field and Zeeman regimes are simultaneously realized, and we argue that the border between these two regions is where spin domains and phase defects are generated. We propose a method to experimentally tune the position of this border

Planetesimal disk evolution driven by embryo-planetesimal gravitational scattering

The process of gravitational scattering of planetesimals by a massive protoplanetary embryo is explored theoretically. We propose a method to describe the evolution of the disk surface density, eccentricity, and inclination caused by the embryo-planetesimal interaction. It relies on the analytical treatment of the scattering in two extreme regimes of the planetesimal epicyclic velocities: shear-dominated (dynamically ``cold'') and dispersion-dominated (dynamically ``hot''). In the former, planetesimal scattering can be treated as a deterministic process. In the latter, scattering is mostly weak because of the large relative velocities of interacting bodies. This allows one to use the Fokker-Planck approximation and the two-body approximation to explore the disk evolution. We compare the results obtained by this method with the outcomes of the direct numerical integrations of planetesimal orbits and they agree quite well. In the intermediate velocity regime an approximate treatment of the disk evolution is proposed based on interpolation between the two extreme regimes. We also calculate the rate of embryo's mass growth in an inhomogeneous planetesimal disk and demonstrate that it is in agreement with both the simulations and earlier calculations. Finally we discuss the question of the direction of the embryo-planetesimal interaction in the dispersion-dominated regime and demonstrate that it is repulsive. This means that the embryo always forms a gap in the disk around it, which is in contrast with the results of other authors. The machinery developed here will be applied to realistic protoplanetary systems in future papers.Comment: 40 pages, 9 figures, submitted to A

Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?

We perform a comprehensive analysis of the spectral statistics of the molecular resonances in $^{166}$Er and $^{168}$Er observed in recent ultracold collision experiments [Frisch et al., Nature {\bf 507}, 475 (2014)] with the aim of determining the chaoticity of this system. We calculate different independent statistical properties to check their degree of agreement with random matrix theory (RMT), and analyze if they are consistent with the possibility of having missing resonances. The analysis of the short-range fluctuations as a function of the magnetic field points to a steady increase of chaoticity until $B \sim 30$ G. The repulsion parameter decreases for higher magnetic fields, an effect that can be interpreted as due to missing resonances. The analysis of long-range fluctuations allows us to be more quantitative and estimate a $20-25\%$ fraction of missing levels. Finally, a study of the distribution of resonance widths provides additional evidence supporting missing resonances of small width compared with the experimental magnetic field resolution. We conclude that further measurements with increased resolution will be necessary to give a final answer to the problem of missing resonances and the agreement with RMT.Comment: 9 pages, 6 figure

Generalized Miller Formulae

We derive the spectral dependence of the non-linear susceptibility of any order, generalizing the common form of Sellmeier equations. This dependence is fully defined by the knowledge of the linear dispersion of the medium. This finding generalizes the Miller formula to any order of non-linearity. In the frequency-degenerate case, it yields the spectral dependence of non-linear refractive indices of arbitrary order.Comment: 12 pages, 1 figure (4 panels

Good rotations

Numerical integrations in celestial mechanics often involve the repeated computation of a rotation with a constant angle. A direct evaluation of these rotations yields a linear drift of the distance to the origin. This is due to roundoff in the representation of the sine s and cosine c of the angle theta. In a computer, one generally gets c^2 + s^2 1, resulting in a mapping that is slightly contracting or expanding. In the present paper we present a method to find pairs of representable real numbers s and c such that c^2 + s^2 is as close to 1 as possible. We show that this results in a drastic decrease of the systematic error, making it negligible compared to the random error of other operations. We also verify that this approach gives good results in a realistic celestial mechanics integration.Comment: 24 pages, 3 figure

The evolution of surface magnetic fields in young solar-type stars

The surface rotation rates of young solar-type stars decrease rapidly with age from the end of the pre-main sequence though the early main sequence. This suggests that there is also an important change in the dynamos operating in these stars, which should be observable in their surface magnetic fields. Here we present early results in a study aimed at observing the evolution of these magnetic fields through this critical time period. We are observing stars in open clusters and stellar associations to provide precise ages, and using Zeeman Doppler Imaging to characterize the complex magnetic fields. Presented here are results for six stars, three in the in the beta Pic association (~10 Myr old) and three in the AB Dor association (~100 Myr old).Comment: To appear in the proceedings of IAU symposium 302: Magnetic fields throughout stellar evolution. 2 pages, 3 figure

A Possible Divot in the Size Distribution of the Kuiper Belt's Scattering Objects

Via joint analysis of a calibrated telescopic survey, which found scattering Kuiper Belt objects, and models of their expected orbital distribution, we measure the form of the scattering object's size distribution. Ruling out a single power-law at greater than 99% confidence, we constrain the form of the size distribution and find that, surprisingly, our analysis favours a very sudden decrease (a divot) in the number distribution as diameters decrease below 100 km, with the number of smaller objects then rising again as expected via collisional equilibrium. Extrapolating at this collisional equilibrium slope produced enough kilometer-scale scattering objects to supply the nearby Jupiter-Family comets. Our interpretation is that this divot feature is a preserved relic of the size distribution made by planetesimal formation, now "frozen in" to portions of the Kuiper Belt sharing a "hot" orbital inclination distribution, explaining several puzzles in Kuiper Belt science. Additionally, we show that to match today's scattering-object inclination distribution, the supply source that was scattered outward must have already been vertically heated to of order 10 degrees.Comment: accepted 2013 January 8; published 2013 January 22 21 pages, 4 figure

Density functional study of two-dimensional He-4 clusters

Binding energies and density profiles of two-dimensional systems of liquid He-4 with different geometries are studied by means of a zero-range density functional adjusted to reproduce the line tension obtained in a previous diffusion Monte Carlo calculation (lambda_{DMC}=0.121 K/A). It is shown that this density functional provides accurate results for the binding energy of large clusters with a reasonable computational effort.Comment: RevTeX4, 11 pages + 2 tables + 6 figure