Momentum distributions and numerical methods for strongly interacting one-dimensional spinor gases

One-dimensional spinor gases with strong delta interaction fermionize and form a spin chain. The spatial degrees of freedom of this atom chain can be described by a mapping to spinless noninteracting fermions and the spin degrees of freedom are described by a spin-chain model with nearest-neighbor interactions. Here, we compute momentum and occupation-number distributions of up to 16 strongly interacting spinor fermions and bosons as a function of their spin imbalance, the strength of an externally applied magnetic field gradient, the length of their spin, and for different excited states of the multiplet. We show that the ground-state momentum distributions resemble those of the corresponding noninteracting systems, apart from flat background distributions, which extend to high momenta. Moreover, we show that the spin order of the spin chain---in particular antiferromagnetic spin order---may be deduced from the momentum and occupation-number distributions of the system. Finally, we present efficient numerical methods for the calculation of the single-particle densities and one-body density matrix elements and of the local exchange coefficients of the spin chain for large systems containing more than 20 strongly interacting particles in arbitrary confining potentials.Comment: See the ancillary files for the Mathematica notebook used to calculate the results of this paper, the derivation of the formula for the one-body density matrix elements, given by Eq. (22), and a table with the local exchange coefficients of up to 60 harmonically trapped particles. A less efficient method for calculating the exchange coefficients was given in the 2nd version of this manuscrip

Two-part multiple spell models for health care demand

The demand for certain types of health care services depends on decisions of both the individual and the health care provider. This paper studies the conditions under which it is possible to separately identify the parameters driving the two decision processes using only count data on the total demand. It is found that the frequently used hurdle models may not be adequate to describe this type of demand, especially when the assumption of a single illness spell per observation period is violated. A test for the single spell hypothesis is developed and alternative modelling strategies are suggested, including one that allows for correlated unobserved heterogeneity. The results of the paper are illustrated with an application.

Law of large numbers for non-elliptic random walks in dynamic random environments

We prove a law of large numbers for a class of $\Z^d$-valued random walks in dynamic random environments, including non-elliptic examples. We assume for the random environment a mixing property called \emph{conditional cone-mixing} and that the random walk tends to stay inside wide enough space-time cones. The proof is based on a generalization of a regeneration scheme developed by Comets and Zeitouni for static random environments and adapted by Avena, den Hollander and Redig to dynamic random environments. A number of one-dimensional examples are given. In some cases, the sign of the speed can be determined.Comment: 36 pages, 4 figure

Is it different for zeros? Discriminating between models for non-negative data with many zeros

In many economic applications, the variate of interest is non-negative and its distribution is characterized by a mass-point at zero and a long right-tail. Many regression strategies have been proposed to deal with data of this type. Although there has been a long debate in the literature on the appropriateness of different models, formal statistical tests to choose between the competing specifications, or to assess the validity of the preferred model, are not often used in practice. In this paper we propose a novel and simple regression-based specification test that can be used to test these models against each other.

Antiferromagnetic Heisenberg Spin Chain of a Few Cold Atoms in a One-Dimensional Trap

We report on the deterministic preparation of antiferromagnetic Heisenberg spin chains consisting of up to four fermionic atoms in a one-dimensional trap. These chains are stabilized by strong repulsive interactions between the two spin components without the need for an external periodic potential. We independently characterize the spin configuration of the chains by measuring the spin orientation of the outermost particle in the trap and by projecting the spatial wave function of one spin component on single-particle trap levels. Our results are in good agreement with a spin-chain model for fermionized particles and with numerically exact diagonalizations of the full few-fermion system

Microeconometrics : Editors’ introduction

info:eu-repo/semantics/publishedVersio

Spherical Planetary Nebulae

By examining their mass loss history and their distribution in the galaxy I argue that spherical planetary nebulae (PNe) form a special group among all planetary nebulae. The smooth surface brightness of most spherical PNe suggests that their progenitors did not go through a final intensive wind (FIW, also termed superwind) phase. While 70 per cent of the PNe of all other PNe groups are closer to the galactic center than the sun is, only 30 per cent of spherical PNe are. These, plus the well known high scale height above the galactic plane of spherical PNe, suggest that the progenitors of spherical PNe are low mass stars having low metallicity. Although many stars have these properties, only about 10 per cent of all PNe are spherical. By comparing the galactic distribution of spherical PNe to the metallicity evolution in the galaxy, I find that the critical metallicity above which no spherical PNe are formed is [Fe/H] ~ -0.4. I explain this as well as other properties of spherical PNe in the context of the companion model for shaping PNe, arguing that spherical PNe are formed from stars which had no close companion, stellar or substellar, orbiting them.Comment: 10 pages + 1 table(ps) and 1 figure(ps); Submitted to MNRA