Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

Hopf algebras and characters of classical groups

Schur functions provide an integral basis of the ring of symmetric functions. It is shown that this ring has a natural Hopf algebra structure by identifying the appropriate product, coproduct, unit, counit and antipode, and their properties. Characters of covariant tensor irreducible representations of the classical groups GL(n), O(n) and Sp(n) are then expressed in terms of Schur functions, and the Hopf algebra is exploited in the determination of group-subgroup branching rules and the decomposition of tensor products. The analysis is carried out in terms of n-independent universal characters. The corresponding rings, CharGL, CharO and CharSp, of universal characters each have their own natural Hopf algebra structure. The appropriate product, coproduct, unit, counit and antipode are identified in each case.Comment: 9 pages. Uses jpconf.cls and jpconf11.clo. Presented by RCK at SSPCM'07, Myczkowce, Poland, Sept 200

Risk of cancer following primary total hip replacement or primary resurfacing arthroplasty of the hip : A retrospective cohort study in Scotland

Acknowledgements: We are grateful to Lee Barnsdale, Doug Clark, and Richard Dobbie for advice and assistance with data preparation before analysis, and to the three anonymous referees for their helpful comments and suggestions.Peer reviewedPublisher PD

Covariance, correlation and entanglement

Some new identities for quantum variance and covariance involving commutators are presented, in which the density matrix and the operators are treated symmetrically. A measure of entanglement is proposed for bipartite systems, based on covariance. This works for two- and three-component systems but produces ambiguities for multicomponent systems of composite dimension. Its relationship to angular momentum dispersion for symmetric symmetric spin states is described.Comment: 30 pages, Latex, to appear in J Phys

Advanced engine study program

A design and analysis study was conducted to provide advanced engine descriptions and parametric data for space transfer vehicles. The study was based on an advanced oxygen/hydrogen engine in the 7,500 to 50,000 lbf thrust range. Emphasis was placed on defining requirements for high-performance engines capable of achieving reliable and versatile operation in a space environment. Four variations on the expander cycle were compared, and the advantages and disadvantages of each were assessed. Parametric weight, envelope, and performance data were generated over a range of 7,500 to 50,000 lb thrust and a wide range of chamber pressure and nozzle expansion ratio

First detection of [N II] 205 micrometer absorption in interstellar gas

We present high resolution [NII] 205 micrometer ^3P_1-^3P_0 spectra obtained with Herschel-HIFI towards a small sample of far-infrared bright star forming regions in the Galactic plane: W31C (G10.6-0.4), W49N (G43.2-0.1), W51 (G49.5-0.4), and G34.3+0.1. All sources display an emission line profile associated directly with the HII regions themselves. For the first time we also detect absorption of the [NII] 205 micrometer line by extended low-density foreground material towards W31C and W49N over a wide range of velocities. We attribute this absorption to the warm ionised medium (WIM) and find N(N^+)\approx 1.5x10^17 cm^-2 towards both sources. This is in agreement with recent Herschel-HIFI observations of [CII] 158 micrometer, also observed in absorption in the same sight-lines, if \approx7-10 % of all C^+ ions exist in the WIM on average. Using an abundance ratio of [N]/[H] = 6.76x10^-5 in the gas phase we find that the mean electron and proton volume densities are ~0.1-0.3 cm^-3 assuming a WIM volume filling fraction of 0.1-0.4 with a corresponding line-of-sight filling fraction of 0.46-0.74. A low density and a high WIM filling fraction are also supported by RADEX modelling of the [NII] 205 micrometer absorption and emission together with visible emission lines attributed mainly to the WIM. The detection of the 205 micrometer line in absorption emphasises the importance of a high spectral resolution, and also offers a new tool for investigation of the WIM.Comment: 7 pages, 4 figures, accepted for publication in Astronomy & Astrophysics, 11 June 201

Resolving the shocked gas in HH54 with Herschel: CO line mapping at high spatial and spectral resolution

The HH54 shock is a Herbig-Haro object, located in the nearby Chamaeleon II cloud. Observed CO line profiles are due to a complex distribution in density, temperature, velocity, and geometry. Resolving the HH54 shock wave in the far-infrared cooling lines of CO constrain the kinematics, morphology, and physical conditions of the shocked region. We used the PACS and SPIRE instruments on board the Herschel space observatory to map the full FIR spectrum in a region covering the HH54 shock wave. Complementary Herschel-HIFI, APEX, and Spitzer data are used in the analysis as well. The observed features in the line profiles are reproduced using a 3D radiative transfer model of a bow-shock, constructed with the Line Modeling Engine code (LIME). The FIR emission is confined to the HH54 region and a coherent displacement of the location of the emission maximum of CO with increasing J is observed. The peak positions of the high-J CO lines are shifted upstream from the lower J CO lines and coincide with the position of the spectral feature identified previously in CO(10-9) profiles with HIFI. This indicates a hotter molecular component in the upstream gas with distinct dynamics. The coherent displacement with increasing J for CO is consistent with a scenario where IRAS12500-7658 is the exciting source of the flow, and the 180 K bow-shock is accompanied by a hot (800 K) molecular component located upstream from the apex of the shock and blueshifted by -7 km s$^{-1}$. The spatial proximity of this knot to the peaks of the atomic fine-structure emission lines observed with Spitzer and PACS ([OI]63, 145 $\mu$m) suggests that it may be associated with the dissociative shock as the jet impacts slower moving gas in the HH54 bow-shock.Comment: 6 pages, 5 figure

Exact correlation functions of the BCS model in the canonical ensemble

We evaluate correlation functions of the BCS model for finite number of particles. The integrability of the Hamiltonian relates it with the Gaudin algebra ${\cal G}[sl(2)]$. Therefore, a theorem that Sklyanin proved for the Gaudin model, can be applied. Several diagonal and off-diagonal correlators are calculated. The finite size scaling behavior of the pairing correlation function is studied.Comment: 4 pages revtex; 2 figures .eps. Revised version to be published in Phys. Rev. Let