Classical Supersymmetric Mechanics

We analyse a supersymmetric mechanical model derived from (1+1)-dimensional field theory with Yukawa interaction, assuming that all physical variables take their values in a Grassmann algebra B. Utilizing the symmetries of the model we demonstrate how for a certain class of potentials the equations of motion can be solved completely for any B. In a second approach we suppose that the Grassmann algebra is finitely generated, decompose the dynamical variables into real components and devise a layer-by-layer strategy to solve the equations of motion for arbitrary potential. We examine the possible types of motion for both bosonic and fermionic quantities and show how symmetries relate the former to the latter in a geometrical way. In particular, we investigate oscillatory motion, applying results of Floquet theory, in order to elucidate the role that energy variations of the lower order quantities play in determining the quantities of higher order in B.Comment: 29 pages, 2 figures, submitted to Annals of Physic

The dynamics of vortices on S^2 near the Bradlow limit

The explicit solutions of the Bogomolny equations for N vortices on a sphere of radius R^2 > N are not known. In particular, this has prevented the use of the geodesic approximation to describe the low energy vortex dynamics. In this paper we introduce an approximate general solution of the equations, valid for R^2 close to N, which has many properties of the true solutions, including the same moduli space CP^N. Within the framework of the geodesic approximation, the metric on the moduli space is then computed to be proportional to the Fubini- Study metric, which leads to a complete description of the particle dynamics.Comment: 17 pages, 9 figure

Remarks on gauge vortex scattering

In the abelian Higgs model, among other situations, it has recently been realized that the head-on scattering of $n$ solitons distributed symmetrically around the point of scattering is by an angle $\pi/n$, independant of various details of the scattering. In this note, it is first observed that this result is in fact not entirely surprising: the above is one of only two possible outcomes. Then, a generalization of an argument given by Ruback for the case of two gauge theory vortices in the Bogomol'nyi limit is used to show that in the geodesic approximation the above result follows from purely geometric considerations.Comment: 6 pages, revtex, missing authors added to one referenc

Calogero-Moser Models V: Supersymmetry and Quantum Lax Pair

It is shown that the Calogero-Moser models based on all root systems of the finite reflection groups (both the crystallographic and non-crystallographic cases) with the rational (with/without a harmonic confining potential), trigonometric and hyperbolic potentials can be simply supersymmetrised in terms of superpotentials. There is a universal formula for the supersymmetric ground state wavefunction. Since the bosonic part of each supersymmetric model is the usual quantum Calogero-Moser model, this gives a universal formula for its ground state wavefunction and energy, which is determined purely algebraically. Quantum Lax pair operators and conserved quantities for all the above Calogero-Moser models are established.Comment: LaTeX2e, 31 pages, no figure

Reparametrising the Skyrme Model using the Lithium-6 Nucleus

The minimal energy B=6 solution of the Skyrme model is a static soliton with $D_{4d}$ symmetry. The symmetries of the solution imply that the quantum numbers of the ground state are the same as those of the Lithium-6 nucleus. This identification is considered further by obtaining expressions for the mean charge radius and quadrupole moment, dependent only on the Skyrme model parameters $e$ (a dimensionless constant) and $F_\pi$ (the pion decay constant). The optimal values of these parameters have often been deliberated upon, and we propose, for $B>2$, changing them from those which are most commonly accepted. We obtain specific values for these parameters for B=6, by matching with properties of the Lithium-6 nucleus. We find further support for the new values by reconsidering the $\alpha$-particle and deuteron as quantized B=4 and B=2 Skyrmions.Comment: 18 page

New results on twinlike models

In this work we study the presence of kinks in models described by a single real scalar field in bidimensional spacetime. We work within the first-order framework, and we show how to write first-order differential equations that solve the equations of motion. The first-order equations strongly simplify the study of linear stability, which is implemented on general grounds. They also lead to a direct investigation of twinlike theories, which is used to introduce a family of models that support the same defect structure, with the very same energy density and linear stability.Comment: 6 pages, 1 figur

Social/health maintenance organization and fee-for-service health outcomes over time.

Evaluating the performance of long-term care (LTC) demonstrations requires longitudinal assessment of multiple outcomes where selective mortality and disenrollment, if not accounted for, can give the appearance of reduced (or enhanced) efficacy. We assessed outcomes in social/health maintenance organizations (S/HMOs) and Medicare fee-for-service (FFS) care using a multivariate model to estimate active life expectancy (ALE). S/HMO enrollees and samples of FFS clients in four sites were analyzed and outcome differences assessed for a 3-year period. Results provide insights into S/HMO performance under different conditions and, more generally, into evaluating LTC demonstrations without randomized client and control groups

Performance of Electropun Polyacrylonitrile Nanofibrous Phases, Shown for the Separation of Water-Soluble Food Dyes via UTLC-Vis-ESI-MS

Research in the miniaturization of planar chromatography led to various approaches in manufacturing ultrathin-layer chromatography (UTLC) layers of reduced thickness (<50 µm) along with smaller instrumentation, as targeted in Office Chromatography. This novel concept merges 3D print & media technologies with miniaturized planar chromatography to realize an all-in-one instrument, in which all steps of UTLC are automated and integrated in the same tiny device. In this context, the development of electrospun polyacrylonitrile (PAN) nanofiber phases was investigated as well as its performance. A nanofibrous stationary phase with fiber diameters of 150–225 nm and a thickness of ca. 25 µm was manufactured. Mixtures of water-soluble food dyes were printed on it using a modified office printer, and successfully separated to illustrate the capabilities of such UTLC media. The separation took 8 min for 30 mm and was faster (up to a factor of 2) than on particulate layers. The mean hRF values ranging from 25 to 90 for the five food dyes were well spread over the migration distance, with an overall reproducibility of 7% (mean %RSD over 5 different plates for 5 dyes). The individual mean plate numbers over 5 plates ranged between 8286 and 22,885 (mean of 11,722 over all 5 dyes). The single mean resolutions RS were between 1.7 and 6.5 (for the 5 food dyes over 5 plates), with highly satisfying reproducibilities (0.3 as mean deviation of RS). Using videodensitometry, different amounts separated in parallel led to reliable linear calibrations for each dye (sdv of 3.1–9.1% for peak heights and 2.4–9.3% for peak areas). Coupling to mass spectrometry via an elution head-based interface was successfully demonstrated for such ultrathin layers, showing several advantages such as a reduced cleaning process and a minimum zone distance. All these results underline the potential of electrospun nanofibrous phases to succeed as affordable stationary phase for quantitative UTLC

Angularly localized Skyrmions

Quantized Skyrmions with baryon numbers $B=1,2$ and 4 are considered and angularly localized wavefunctions for them are found. By combining a few low angular momentum states, one can construct a quantum state whose spatial density is close to that of the classical Skyrmion, and has the same symmetries. For the B=1 case we find the best localized wavefunction among linear combinations of $j=1/2$ and $j=3/2$ angular momentum states. For B=2, we find that the $j=1$ ground state has toroidal symmetry and a somewhat reduced localization compared to the classical solution. For B=4, where the classical Skyrmion has cubic symmetry, we construct cubically symmetric quantum states by combining the $j=0$ ground state with the lowest rotationally excited $j=4$ state. We use the rational map approximation to compare the classical and quantum baryon densities in the B=2 and B=4 cases.Comment: 22 page