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

The XMM-Newton Detection of Diffuse Inverse Compton X-rays from Lobes of the FR-II Radio Galaxy 3C98

The XMM-Newton observation of the nearby FR-II radio galaxy 3C 98 is reported. In two exposures on the target, faint diffuse X-ray emission associated with the radio lobes was significantly detected, together with a bright X-ray active nucleus, of which the 2 -- 10 keV intrinsic luminosity is (4 -- 8) \times 10^{42} erg s-1. The EPIC spectra of the northern and southern lobes are reproduced by a single power law model modified by the Galactic absorption, with a photon index of 2.2-0.5+0.6 and 1.7-0.6+0.7 respectively. These indices are consistent with that of the radio synchrotron spectrum, 1.73 +- 0.01 The luminosity of the northern and southern lobes are measured to be 8.3-2.6+3.3 \times 10^{40} erg s-1 and 9.2-4.3+5.7 \times 10^{40} erg s-1, respectively, in the 0.7 -- 7 keV range. The diffuse X-ray emission is interpreted as an inverse-Compton emission, produced when the synchrotron-emitting energetic electrons in the lobes scatter off the cosmic microwave background photons. The magnetic field in the lobes is calculated to be about 1.7 \mu G, which is about 2.5 times lower than the value estimated under the minimum energy condition. The energy density of the electrons is inferred to exceed that in the magnetic fields by a factor of 40 -- 50.Comment: 23 pages, 7 figures. Accepted for publication in the Astrophysical Journa

Evolving Roles and Structures of Triadic Engagement in Healthcare

Purpose This study focuses on the changing nature of healthcare service encounters by studying the phenomenon of triadic engagement incorporating interactions between patients, local and virtual networks and healthcare professionals. Design/methodology/approach An 18-month longitudinal ethnographic study documents interactions in naturally occurring healthcare consultations. Professionals (n=13) and patients (n=24) within primary and secondary care units were recruited. Analysis of observations, field notes and interviews provides an integrated picture of triadic engagement. Findings Triadic engagement is conceptualised against a two-level framework. (1) The structure of triadic consultations is identified in terms of the human voice, virtual voice and networked voice. These are related to: companions’ contributions to discussions and the virtual network impact. (2) Evolving roles are mapped to three phases of transformation: enhancement; empowerment; emancipation. Triadic engagement varied across conditions. Research limitations/implications These changing roles and structures evidence an increasing emphasis on the responsible consumer and patients/companions to utilise information/support in making health-related decisions. The nature and role of third voices requires clear delineation. Practical implications Structures of consultations should be rethought around the diversity of patient/companion behaviours and expectations as patients undertake self-service activities. Implications for policy and practice are: the parallel set of local/virtual informational and service activities; a network orientation to healthcare; tailoring of support resources/guides for professionals and third parties to inform support practices. Originality/value Contributions are made to understanding triadic engagement and forwarding the agenda on patient-centred care. Longitudinal illumination of consultations is offered through an exceptional level of access to observe consultations

A Chandra detection of diffuse hard X-ray emission associated with the lobes of the radio galaxy 3C 452

An 80 ksec Chandra ACIS observation of the radio galaxy 3C 452 is reported. A diffuse X-ray emission associated with the lobes has been detected with high statistical significance, together with the X-ray nucleus of the host galaxy. The 0.5--5 keV ACIS spectrum of the diffuse emission is described by a two-component model, consisting of a soft thermal plasma emission from the host galaxy halo and a hard non-thermal power-law component. The hard component is ascribed to the inverse Comptonization of cosmic microwave background photons by the synchrotron emitting electrons in the lobes, because its spectral energy index, 0.68+-0.28, is consistent with the radio synchrotron index, 0.78. These results reveal a significant electron dominance in the lobes. The electrons are inferred to have a relatively uniform distribution, while the magnetic field is compressed toward the lobe periphery.Comment: 4 figures, 2 tables, Accepted by ApJL (to appear in the December 1 issue

Multifrequency Polarimetry of the Nrao 140 Jet: Possible Detection of a Helical Magnetic Field and Constraints on its Pitch Angle

We present results from multifrequency polarimetry of NRAO 140 using the Very Long Baseline Array. These observations allow us to reveal the distributions of both the polarization position angle and the Faraday rotation measure (RM). These distributions are powerful tools to discern the projected and line-of-sight components of the magnetic field, respectively. We find a systematic gradient in the RM distribution, with its sign being opposite at either side of the jet with respect to the jet axis. The sign of the RM changes only with the direction of the magnetic field component along the line of sight, so this can be explained by the existence of helical magnetic components associated with the jet itself. We derive two constraints for the pitch angle of the helical magnetic field from the distributions of the RM and the projected magnetic field; the RM distribution indicates that the helical fields are tightly wound, while that of the projected magnetic field suggests they are loosely wound around the jet axis. This inconsistency may be explained if the Faraday rotator is not cospatial with theemitting region. Our results may point toward a physical picture in which an ultra-relativistic jet (spine) with a loosely wound helical magnetic field is surrounded by a sub-relativistic wind layer (sheath) with a tightly wound helical magnetic field.Comment: 12 pages, 4 figures, ApJ, in pres

Direct Distance Measurements to Superluminal Radio Sources

We present a new technique for directly measuring the distances to superluminal radio sources. By comparing the observed proper motions of components in a parsec scale radio jet to their measured Doppler factors, we can deduce the distance to the radio source independent of the standard rungs in the cosmological distance ladder. This technique requires that the jet angle to the line of sight and the ratio of pattern to flow velocities are sufficiently constrained. We evaluate a number of possibilities for constraining these parameters and demonstrate the technique on a well defined component in the parsec scale jet of the quasar 3C279 (z = 0.536). We find an angular size distance to 3C279 of greater than 1.8 (+0.5,-0.3) n^{1/8} Gpc, where n is the ratio of the energy density in the magnetic field to the energy density in the radiating particles in that jet component. For an Einstein-de Sitter Universe, this measurement would constrain the Hubble constant to be H < 65 n^{-1/8} km/s/Mpc at the two sigma level. Similar measurements on higher redshift sources may help discriminate between cosmological models.Comment: 18 pages, 8 figures, to be published in The Astrophysical Journa

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

A genomic view of the NOD-like receptor family in teleost fish: identification of a novel NLR subfamily in zebrafish

<p>Abstract</p> <p>Background</p> <p>A large multigene family of NOD-like receptor (NLR) molecules have been described in mammals and implicated in immunity and apoptosis. Little information, however, exists concerning this gene family in non-mammalian taxa. This current study, therefore, provides an in-depth investigation of this gene family in lower vertebrates including extensive phylogenetic comparison of zebrafish NLRs with orthologs in tetrapods, and analysis of their tissue-specific expression.</p> <p>Results</p> <p>Three distinct NLR subfamilies were identified by mining genome databases of various non-mammalian vertebrates; the first subfamily (NLR-A) resembles mammalian NODs, the second (NLR-B) resembles mammalian NALPs, while the third (NLR-C) appears to be unique to teleost fish. In zebrafish, NLR-A and NLR-B subfamilies contain five and six genes respectively. The third subfamily is large, containing several hundred NLR-C genes, many of which are predicted to encode a C-terminal B30.2 domain. This subfamily most likely evolved from a NOD3-like molecule. Gene predictions for zebrafish NLRs were verified using sequence derived from ESTs or direct sequencing of cDNA. Reverse-transcriptase (RT)-PCR analysis confirmed expression of representative genes from each subfamily in selected tissues.</p> <p>Conclusion</p> <p>Our findings confirm the presence of multiple NLR gene orthologs, which form a large multigene family in teleostei. Although the functional significance of the three major NLR subfamilies is unclear, we speculate that conservation and abundance of NLR molecules in all teleostei genomes, reflects an essential role in cellular control, apoptosis or immunity throughout bony fish.</p

On the informational content of wage offers

This article investigates signaling and screening roles of wage offers in a single-play matching model with two-sided unobservable characteristics. It generates the following predictions as matching equilibrium outcomes: (i) “good” jobs offer premia if “high-quality” worker population is large; (ii) “bad” jobs pay compensating differentials if the proportion of “good” jobs to “low-quality” workers is large; (iii) all firms may offer a pooling wage in markets dominated by “high-quality” workers and firms; or (iv) Gresham’s Law prevails: “good” types withdraw if “bad” types dominate the population. The screening/signaling motive thus has the potential of explaining a variety of wage patterns