On the Use of Group Theoretical and Graphical Techniques toward the Solution of the General N-body Problem

Group theoretic and graphical techniques are used to derive the N-body wave function for a system of identical bosons with general interactions through first-order in a perturbation approach. This method is based on the maximal symmetry present at lowest order in a perturbation series in inverse spatial dimensions. The symmetric structure at lowest order has a point group isomorphic with the S_N group, the symmetric group of N particles, and the resulting perturbation expansion of the Hamiltonian is order-by-order invariant under the permutations of the S_N group. This invariance under S_N imposes severe symmetry requirements on the tensor blocks needed at each order in the perturbation series. We show here that these blocks can be decomposed into a basis of binary tensors invariant under S_N. This basis is small (25 terms at first order in the wave function), independent of N, and is derived using graphical techniques. This checks the N^6 scaling of these terms at first order by effectively separating the N scaling problem away from the rest of the physics. The transformation of each binary tensor to the final normal coordinate basis requires the derivation of Clebsch-Gordon coefficients of S_N for arbitrary N. This has been accomplished using the group theory of the symmetric group. This achievement results in an analytic solution for the wave function, exact through first order, that scales as N^0, effectively circumventing intensive numerical work. This solution can be systematically improved with further analytic work by going to yet higher orders in the perturbation series.Comment: This paper was submitted to the Journal of Mathematical physics, and is under revie

Synthesis and Properties of Dipyridylcyclopentenes

A short and general route to the substituted dipyridylcyclopentenes was explored and several new compounds belonging to this new group of diarylethenes were synthesized. The study of their photochromic and thermochromic properties shows that the rate of the thermal ring opening is strongly dependent on the polarity of the solvent.

Correlation length scalings in fusion edge plasma turbulence computations

The effect of changes in plasma parameters, that are characteristic near or at an L-H transition in fusion edge plasmas, on fluctuation correlation lengths are analysed by means of drift-Alfven turbulence computations. Scalings by density gradient length, collisionality, plasma beta, and by an imposed shear flow are considered. It is found that strongly sheared flows lead to the appearence of long-range correlations in electrostatic potential fluctuations parallel and perpendicular to the magnetic field.Comment: Submitted to "Plasma Physics and Controlled Fusion

Analytic, Group-Theoretic Density Profiles for Confined, Correlated N-Body Systems

Confined quantum systems involving $N$ identical interacting particles are to be found in many areas of physics, including condensed matter, atomic and chemical physics. A beyond-mean-field perturbation method that is applicable, in principle, to weakly, intermediate, and strongly-interacting systems has been set forth by the authors in a previous series of papers. Dimensional perturbation theory was used, and in conjunction with group theory, an analytic beyond-mean-field correlated wave function at lowest order for a system under spherical confinement with a general two-body interaction was derived. In the present paper, we use this analytic wave function to derive the corresponding lowest-order, analytic density profile and apply it to the example of a Bose-Einstein condensate.Comment: 15 pages, 2 figures, accepted by Physics Review A. This document was submitted after responding to a reviewer's comment

Feasibility study of a synthesis procedure for array feeds to improve radiation performance of large distorted reflector antennas

The topics covered include the following: (1) performance analysis of the Gregorian tri-reflector; (2) design and performance of the type 6 reflector antenna; (3) a new spherical main reflector system design; (4) optimization of reflector configurations using physical optics; (5) radiometric array design; and (7) beam efficiency studies

Element specific characterization of heterogeneous magnetism in (Ga,Fe)N films

We employ x-ray spectroscopy to characterize the distribution and magnetism of particular alloy constituents in (Ga,Fe)N films grown by metal organic vapor phase epitaxy. Furthermore, photoelectron microscopy gives direct evidence for the aggregation of Fe ions, leading to the formation of Fe-rich nanoregions adjacent to the samples surface. A sizable x-ray magnetic circular dichroism (XMCD) signal at the Fe L-edges in remanence and at moderate magnetic fields at 300 K links the high temperature ferromagnetism with the Fe(3d) states. The XMCD response at the N K-edge highlights that the N(2p) states carry considerable spin polarization. We conclude that FeN{\delta} nanocrystals, with \delta > 0.25, stabilize the ferromagnetic response of the films.Comment: 4 pages, 3 figures, 1 tabl

Feshbach Resonance Cooling of Trapped Atom Pairs

Spectroscopic studies of few-body systems at ultracold temperatures provide valuable information that often cannot be extracted in a hot environment. Considering a pair of atoms, we propose a cooling mechanism that makes use of a scattering Feshbach resonance. Application of a series of time-dependent magnetic field ramps results in the situation in which either zero, one, or two atoms remain trapped. If two atoms remain in the trap after the field ramps are completed, then they have been cooled. Application of the proposed cooling mechanism to optical traps or lattices is considered.Comment: 5 pages, 3 figures; v.2: major conceptual change