Royal Holloway Research Online

    A classical treatment of the quadratic Zeeman effect in atomic hydrogen

    Get PDF
    The classical Hamiltonian describing the hydrogen atom in the presence of a static magnetic field of arbitrary strength for arbitrary angular momentum is derived. For this Hamiltonian the transition from the regular to the chaotic motion is observed by means of the Poincare mappings. Two different classes of non-planar periodic orbits are traced in both regular and irregular regions. The bifurcations and variation of the periodic motion with the change of the total energy parameter throughout the regular regime and into the chaotic regime are given together with the relevant frequencies. For both classes the stability/instability of the periodic orbits is studied by calculating the linearization matrix in the neighbourhood of the corresponding fixed points of the Poincare mappings. In one class, the class of orbits that approach very close to the nucleus, we have surprisingly found that a set of periodic orbits bifurcate from the same periodic orbit along the field at various values of the energy. These values are determined numerically. A repeated pattern of stability and instability of these orbits exists over decreasing intervals of energy until the escape energy is approached. All these periodic orbits are unstable beyond the ionization limit. On the other hand we have found that the bifurcation of the second class of orbits is, generally, generic. Three sets of the energy separation lines due to three types of periodic motions are given when B = 60 kG with m - 0. Other sets of lines are given for B = 42 kG with m = 0, m = -1 and m = -2. Many of these lines coincide with the spectral lines obtained experimentally by A. Holle et al (1986).The energy spacing 0.64 near the ionisation limit, which has been found recently in the experiments of Holle et al (1986) is due to one of the non-planar orbits. Other new predicted spacings arising from other orbits have been seen in high resolution experiments on atoms in external fields (Main et al 1986).<p

    Stress and Diabetes

    No full text

    The NRAMP Impact Assessment Report

    No full text

    The asymptotic relative entropy of entanglement

    No full text
    We present an analytical formula for the asymptotic relative entropy of entanglement for Werner states of arbitrary dimension. We then demonstrate its validity using methods from convex optimization. To our knowledge, this is the first case in which the value of a subadditive entanglement measure has been obtained in the asymptotic limit

    First dark matter search results from a 4-kg CF$_3$I bubble chamber operated in a deep underground site

    No full text
    New data are reported from the operation of a 4.0 kg CF$_{3}$I bubble chamber in the 6800-foot-deep SNOLAB underground laboratory. The effectiveness of ultrasound analysis in discriminating alpha-decay background events from single nuclear recoils has been confirmed, with a lower bound of $>$99.3% rejection of alpha-decay events. Twenty single nuclear recoil event candidates and three multiple bubble events were observed during a total exposure of 553 kg-days distributed over three different bubble nucleation thresholds. The effective exposure for single bubble recoil-like events was 437.4 kg-days. A neutron background internal to the apparatus, of known origin, is estimated to account for five single nuclear recoil events and is consistent with the observed rate of multiple bubble events. This observation provides world best direct detection constraints on WIMP-proton spin-dependent scattering for WIMP masses $>$20 GeV/c$^{2}$ and demonstrates significant sensitivity for spin-independent interactions

    Monoidal Computer I: Basic Computability by String Diagrams

    No full text
    We present a new model of computation, described in terms of monoidal categories. It conforms the Church-Turing Thesis, and captures the same computable functions as the standard models. It provides a succinct categorical interface to most of them, free of their diverse implementation details, using the ideas and structures that in the meantime emerged from research in semantics of computation and programming. The salient feature of the language of monoidal categories is that it is supported by a sound and complete graphical formalism, string diagrams, which provide a concrete and intuitive interface for abstract reasoning about computation. The original motivation and the ultimate goal of this effort is to provide a convenient high level programming language for a theory of computational resources, such as one-way functions, and trapdoor functions, by adopting the methods for hiding the low level implementation details that emerged from practice. In the present paper, we make the initial step towards this ambitious goal, and sketch the ideas how to reach it. These ideas will be elaborated in the three sequel papers, that are in preparation

    Magnet: Practical Subscription Clustering for Internet-Scale Publish/Subscribe

    No full text
    An effective means for building Internet-scale distributed applications, and in particular those involving group-based information sharing, is to deploy peer-to-peer overlay networks. The key pre-requisite for supporting these types of applications on top of the overlays is efficient distribution of messages to multiple subscribers dispersed across numerous multicast groups. In this paper, we introduce Magnet: a peer-to-peer publish/subscribe system which achieves efficient message distribution by dynamically organizing peers with similar subscriptions into dissemination structures which preserve locality in the subscription space. Magnet is able to significantly reduce the message propagation costs by taking advantage of subscription correlations present in many large-scale group-based applications. We evaluate Magnet by comparing its performance against a strawman pub/sub system which does not cluster similar subscriptions by simulation. We find that Magnet outperforms the strawman by a substantial margin on clustered subscription workloads produced using both generative models and real application traces
    Royal Holloway Research Online is based in GB