Low error measurement-free phase gates for qubus computation

We discuss the desired criteria for a two-qubit phase gate and present a method for realising such a gate for quantum computation that is measurement-free and low error. The gate is implemented between qubits via an intermediate bus mode. We take a coherent state as the bus and use cross-Kerr type interactions between the bus and the qubits. This new method is robust against parameter variations and is thus low error. It fundamentally improves on previous methods due its deterministic nature and the lack of approximations used in the geometry of the phase rotations. This interaction is applicable both to solid state and photonic qubit systems.Comment: 6 pages, 4 figures. Published versio

A family of solutions of certain nonautonomous differential equations by series of exponential functions

Solution of differential equations by series of exponential function

On solutions of differential and functional equations Final report

Solutions of differential and functional equation

Random Field XY Model in Three Dimensions: The Role of Vortices

We study vortex states in a 3d random-field XY model of up to one billion lattice spins. Starting with random spin orientations, the sample freezes into the vortex-glass state with a stretched-exponential decay of spin correlations, having short correlation length and a low susceptibility, compared to vortex-free states. In a field opposite to the initial magnetization, peculiar topological objects -- walls of spins still opposite to the field -- emerge along the hysteresis curve. On increasing the field strength, the walls develop cracks bounded by vortex loops. The loops then grow in size and eat the walls away. Applications to magnets and superconductors are discussed.Comment: 5 pages, 8 figure

The Age, Metallicity and Alpha-Element Abundance of Galactic Globular Clusters from Single Stellar Population Models

Establishing the reliability with which stellar population parameters can be measured is vital to extragalactic astronomy. Galactic GCs provide an excellent medium in which to test the consistency of Single Stellar Population (SSP) models as they should be our best analogue to a homogeneous (single) stellar population. Here we present age, metallicity and $\alpha$-element abundance measurements for 48 Galactic globular clusters (GCs) as determined from integrated spectra using Lick indices and SSP models from Thomas, Maraston & Korn, Lee & Worthey and Vazdekis et al. By comparing our new measurements to independent determinations we are able to assess the ability of these SSPs to derive consistent results -- a key requirement before application to heterogeneous stellar populations like galaxies. We find that metallicity determinations are extremely robust, showing good agreement for all models examined here, including a range of enhancement methods. Ages and $\alpha$-element abundances are accurate for a subset of our models, with the caveat that the range of these parameters in Galactic GCs is limited. We are able to show that the application of published Lick index response functions to models with fixed abundance ratios allows us to measure reasonable $\alpha$-element abundances from a variety of models. We also examine the age-metallicity and [$\alpha$/Fe]-metallicity relations predicted by SSP models, and characterise the possible effects of varied model horizontal branch morphology on our overall results.Comment: 22 pages, 19 figures, accepted for publication in MNRA

Mean flow instabilities of two-dimensional convection in strong magnetic fields

The interaction of magnetic fields with convection is of great importance in astrophysics. Two well-known aspects of the interaction are the tendency of convection cells to become narrow in the perpendicular direction when the imposed field is strong, and the occurrence of streaming instabilities involving horizontal shears. Previous studies have found that the latter instability mechanism operates only when the cells are narrow, and so we investigate the occurrence of the streaming instability for large imposed fields, when the cells are naturally narrow near onset. The basic cellular solution can be treated in the asymptotic limit as a nonlinear eigenvalue problem. In the limit of large imposed field, the instability occurs for asymptotically small Prandtl number. The determination of the stability boundary turns out to be surprisingly complicated. At leading order, the linear stability problem is the linearisation of the same nonlinear eigenvalue problem, and as a result, it is necessary to go to higher order to obtain a stability criterion. We establish that the flow can only be unstable to a horizontal mean flow if the Prandtl number is smaller than order , where B0 is the imposed magnetic field, and that the mean flow is concentrated in a horizontal jet of width in the middle of the layer. The result applies to stress-free or no-slip boundary conditions at the top and bottom of the layer