Harmonic Shears and Numerical Conformal Mappings

In this article we introduce a numerical algorithm for finding harmonic mappings by using the shear construction introduced by Clunie and Sheil-Small in 1984. The MATLAB implementation of the algorithm is based on the numerical conformal mapping package, the Schwarz-Christoffel toolbox, by T. Driscoll. Several numerical examples are given. In addition, we discuss briefly the minimal surfaces associated with harmonic mappings and give a numerical example of minimal surfaces.Comment: 15 pages, 6 figure

Spin gravitational resonance and graviton detection

We develop a gravitational analogue of spin magnetic resonance, called spin gravitational resonance, whereby a gravitational wave interacts with a magnetic field to produce a spin transition. In particular, an external magnetic field separates the energy spin states of a spin-1/2 particle, and the presence of the gravitational wave produces a perturbation in the components of the magnetic field orthogonal to the gravitational wave propagation. In this framework we test Dyson's conjecture that individual gravitons cannot be detected. Although we find no fundamental laws preventing single gravitons being detected with spin gravitational resonance, we show that it cannot be used in practice, in support of Dyson's conjecture.Comment: 6 pages, 1 figur

Disorder Correlation Frequency Controlled Diffusion in the Jaynes-Cummings-Hubbard Model

We investigate time-dependent stochastic disorder in the one-dimensional Jaynes-Cummings-Hubbard model and show that it gives rise to diffusive behaviour. We find that disorder correlation frequency is effective in controlling the level of diffusivity. In the defectless system the mean squared displacement (MSD), which is a measure of the diffusivity, increases with increasing disorder frequency. Contrastingly, when static defects are present the MSD increases with disorder frequency only at lower frequencies; at higher frequencies, increasing disorder frequency actually reduces the MSD

Gravitational Casimir effect

We derive the gravitonic Casimir effect with non-idealised boundary conditions. This allows the quantification of the gravitonic contribution to the Casimir effect from real bodies. We quantify the meagreness of the gravitonic Casimir effect in ordinary matter. We also quantify the enhanced effect produced by the speculated Heisenberg-Couloumb (H-C) effect in superconductors, thereby providing a test for the validity of the H-C theory, and consequently the existence of gravitons.Comment: 6 pages, 2 figure

Foldy-Wouthuysen transformation of the generalised Dirac Hamiltonian in a gravitational-wave background

Goncalves et al. derived a non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using the exact Foldy-Wouthuysen transformation. This gave rise to the intriguing notion that spin-precession may occur even in the absence of a magnetic field. We argue that this effect is not physical as it is the result of a gauge-variant term that was an artefact of a flawed application of the exact Foldy-Wouthuysen transformation. In this paper we derive the correct non-relativistic limit of the generalised Dirac Hamiltonian in the presence of a gravitational wave, using both the exact and standard Foldy-Wouthuysen transformation. We show that both transformations consistently produce a Hamiltonian where all terms are gauge-invariant. Unfortunately however, we also show that this means the novel spin-precession effect does not exist.Comment: 4 page

The impact of access to credit on household welfare in rural Vietnam

In this paper, we investigate the determinants of household borrowing from the formal financial sector, the determinants of credit rationing by the formal sector and the impact of credit on household welfare in rural Vietnam. We find that education, savings, the area devoted to farming and the availability of formal credit are important determinants of both household borrowing and credit rationing by the formal sector. We also find that credit has a positive (albeit small) effect on household welfare in rural Vietnam. Our findings have policy implications for land and banking sector reform