Constructing N-qubit entanglement monotones from anti-linear operators

We present a method to construct entanglement measures for pure states of multipartite qubit systems. The key element of our approach is an antilinear operator that we call {\em comb} in reference to the {\em hairy-ball theorem}. For qubits (or spin 1/2) the combs are automatically invariant under SL(2,\CC). This implies that the {\em filters} obtained from the combs are entanglement monotones by construction. We give alternative formulae for the concurrence and the 3-tangle as expectation values of certain antilinear operators. As an application we discuss inequivalent types of genuine four-qubit entanglement.Comment: 5 pages, revtex4; more detailed illustration of the metho

Strategic maritime container transport design in oligopolistic markets

AbstractThis paper considers the maritime container assignment problem in a market setting with two competing firms. Given a series of known, exogenous demands for service between pairs of ports, each company is free to design a liner service network serving a subset of the ports and demand, subject to the size of their fleets and the potential for profit. The model is designed as a three-stage complete information game: in the first stage, the firms simultaneously invest in their fleet; in the second stage, they individually design their networks and solve the route assignment problem with respect to the transport demand they expect to serve, given the fleet determined in the first stage; in the final stage, the firms compete in terms of freight rates on each origin-destination movement. The game is solved by backward induction. Numerical solutions are provided to characterize the equilibria of the game

Dominant mobility modulation by the electric field effect at the LaAlO_3 / SrTiO_3 interface

Caviglia et al. [Nature (London) 456, 624 (2008)] have found that the superconducting LaAlO_3 / SrTiO_3 interface can be gate modulated. A central issue is to determine the principal effect of the applied electric field. Using magnetotransport studies of a gated structure, we find that the mobility variation is almost five times as large as the sheet carrier density. Furthermore, superconductivity can be suppressed at both positive and negative gate bias. These results indicate that the relative disorder strength strongly increases across the superconductor-insulator transition.Comment: 4 pages, 4 figure

Exact Quantum Solutions of Extraordinary N-body Problems

The wave functions of Boson and Fermion gases are known even when the particles have harmonic interactions. Here we generalise these results by solving exactly the N-body Schrodinger equation for potentials V that can be any function of the sum of the squares of the distances of the particles from one another in 3 dimensions. For the harmonic case that function is linear in r^2. Explicit N-body solutions are given when U(r) = -2M \hbar^{-2} V(r) = \zeta r^{-1} - \zeta_2 r^{-2}. Here M is the sum of the masses and r^2 = 1/2 M^{-2} Sigma Sigma m_I m_J ({\bf x}_I - {\bf x}_J)^2. For general U(r) the solution is given in terms of the one or two body problem with potential U(r) in 3 dimensions. The degeneracies of the levels are derived for distinguishable particles, for Bosons of spin zero and for spin 1/2 Fermions. The latter involve significant combinatorial analysis which may have application to the shell model of atomic nuclei. For large N the Fermionic ground state gives the binding energy of a degenerate white dwarf star treated as a giant atom with an N-body wave function. The N-body forces involved in these extraordinary N-body problems are not the usual sums of two body interactions, but nor are forces between quarks or molecules. Bose-Einstein condensation of particles in 3 dimensions interacting via these strange potentials can be treated by this method.Comment: 24 pages, Latex. Accepted for publication in Proceedings of the Royal Societ

Visual Search for Galaxies near the Northern Crossing of the Supergalactic plane by the Milky Way

We have visually examined twelve Palomar red Plates for galaxies at low Galactic latitude b, where the Supergalactic Plane (SGP) is crossed by the Galactic Plane (GP), at Galactic longitude l ~135 degrees. The catalogue consists of 2575 galaxy candidates, of which 462 have major axis diameters d >= 0.8 arc min (uncorrected for extinction). Galaxy candidates can be identified down to |b| ~ 0 degrees. One of our galaxy candidates (J24 = Dwingeloo 1) has recently been discovered independently in 21cm by Kraan-Korteweg et al. (1994) as a nearby galaxy. Comparisons with the structures seen in the IRAS and UGC catalogues are made. We compare the success rate of identifying galaxies using the IRAS Point Source Catalogue under different colour selection criteria. The criteria that require both the 60 micron and 100 micron fluxes to be of high quality, have the highest probability of selecting a galaxy (with d >= 0.6 arc min), but at the expense of selecting a smaller number of galaxies in total.Comment: uuencoded compressed postscript, without figures. The figures are available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

A note on heat and mass transfer from a sphere in Stokes\ud flow at low Péclet number

We consider the low Péclet number, Pe ≪ 1, asymptotic solution for steady-state heat and mass transfer from a sphere immersed in Stokes flow with a Robin boundary condition on its surface, representing Newton cooling or a first-order chemical reaction. The application of van Dyke’s rule up to terms of O(Pe3) shows that the O(Pe3 log Pe) terms in the expression for the average Nusselt/Sherwood number are double those previously derived in the literature. Inclusion of the O(Pe3) terms is shown to increase significantly the range of validity of the expansion

Light Element Abundance Inhomogeneities in Globular Clusters: Probing Star Formation and Evolution in the Early Milky Way

Abundance patterns of the elements C, N, and O are sensitive probes of stellar nucleosynthesis processes and, in addition, O abundances are an important input for stellar age determinations. Understanding the nature of the observed distribution of these elements is key to constraining protogalactic star formation history. Patterns deduced from low-resolution spectroscopy of the CN, CH, NH, and CO molecules for low-mass stars in their core-hydrogen or first shell-hydrogen burning phases in the oldest ensembles known, the Galactic globular star clusters, are reviewed. New results for faint stars in NGC 104 (47 Tuc, C0021-723) reveal that the bimodal, anticorrelated pattern of CN and CH strengths found among luminous evolved stars is also present in stars nearing the end of their main-sequence lifetimes. In the absence of known mechanisms to mix newly synthesized elements from the interior to the observable surface layers of such unevolved stars, those particular inhomogeneities imply that the original material from which the stars formed some 15 billion years ago was chemically inhomogeneous in the C and N elements. However, in other clusters, observations of abundance ratios and C isotope ratios suggest that alterations to surface chemical compositions are produced as stars evolve from the main sequence through the red giant branch. Thus, the current observed distributions of C, N, and O among the brightest stars (those also observed most often) may not reflect the true distribution from which the protocluster cloud formed. The picture which is emerging of the C, N and O abundance patterns within globular clusters may be one whichComment: 12 pages in uuencoded compressed postscript (including figures), to appear in the Canadian Journal of Physics (Special Issue in Honor of G. Herzberg

Large-Scale Structure Shocks at Low and High Redshifts

Cosmological simulations show that, at the present time, a substantial fraction of the gas in the intergalactic medium (IGM) has been shock-heated to T>10^5 K. Here we develop an analytic model to describe the fraction of shocked, moderately overdense gas in the IGM. The model is an extension of the Press & Schechter (1974) description for the mass function of halos: we assume that large-scale structure shocks occur at a fixed overdensity during nonlinear collapse. This in turn allows us to compute the fraction of gas at a given redshift that has been shock-heated to a specified temperature. We show that, if strong shocks occur at turnaround, our model provides a reasonable description of the temperature distribution seen in cosmological simulations at z~0, although it does overestimate the importance of weak shocks. We then apply our model to shocks at high redshifts. We show that, before reionization, the thermal energy of the IGM is dominated by large-scale structure shocks (rather than virialized objects). These shocks can have a variety of effects, including stripping ~10% of the gas from dark matter minihalos, accelerating cosmic rays, and creating a diffuse radiation background from inverse Compton and cooling radiation. This radiation background develops before the first stars form and could have measurable effects on molecular hydrogen formation and the spin temperature of the 21 cm transition of neutral hydrogen. Finally, we show that shock-heating will also be directly detectable by redshifted 21 cm measurements of the neutral IGM in the young universe.Comment: 12 pages, 8 figures, submitted to Ap

New Models of General Relativistic Static Thick Disks

New families of exact general relativistic thick disks are constructed using the ``displace, cut, fill and reflect'' method. A class of functions used to ``fill'' the disks is derived imposing conditions on the first and second derivatives to generate physically acceptable disks. The analysis of the function's curvature further restrict the ranges of the free parameters that allow phisically acceptable disks. Then this class of functions together with the Schwarzschild metric is employed to construct thick disks in isotropic, Weyl and Schwarzschild canonical coordinates. In these last coordinates an additional function must be added to one of the metric coefficients to generate exact disks. Disks in isotropic and Weyl coordinates satisfy all energy conditions, but those in Schwarzschild canonical coordinates do not satisfy the dominant energy condition.Comment: 27 pages, 14 figure