From Andreev bound states to Majorana fermions in topological wires on superconducting substrates : a story of mutation

We study the proximity effect in a topological nanowire tunnel coupled to an s-wave superconducting substrate. We use a general Green's function approach that allows us to study the evolution of the Andreev bound states in the wire into Majorana fermions. We show that the strength of the tunnel coupling induces a topological transition in which the Majorana fermionic states can be destroyed when the coupling is very strong. Moreover, we provide a phenomenologial study of the effects of disorder in the superconductor on the formation of Majorana fermions. We note a non-trivial effect of a quasiparticle broadening term which can take the wire from a topological into a non-topological phase in certain ranges of parameters. Our results have also direct consequences for a nanowire coupled to an inhomogenous superconductor

Effects of finite superconducting coherence lengths and of phase gradients in topological SN and SNS junctions and rings

We study the effect of a finite proximity superconducting (SC) coherence length in SN and SNS junctions consisting of a semiconducting topological insulating wire whose ends are connected to either one or two s-wave superconductors. We find that such systems behave exactly as SN and SNS junctions made from a single wire for which some regions are sitting on top of superconductors, the size of the topological SC region being determined by the SC coherence length. We also analyze the effect of a non-perfect transmission at the NS interface on the spatial extension of the Majorana fermions. Moreover, we study the effects of continuous phase gradients in both an open and closed (ring) SNS junction. We find that such phase gradients play an important role in the spatial localization of the Majorana fermions

Universal Amplitude Ratios of The Renormalization Group: Two-Dimensional Tricritical Ising Model

The scaling form of the free-energy near a critical point allows for the definition of various thermodynamical amplitudes and the determination of their dependence on the microscopic non-universal scales. Universal quantities can be obtained by considering special combinations of the amplitudes. Together with the critical exponents they characterize the universality classes and may be useful quantities for their experimental identification. We compute the universal amplitude ratios for the Tricritical Ising Model in two dimensions by using several theoretical methods from Perturbed Conformal Field Theory and Scattering Integrable Quantum Field Theory. The theoretical approaches are further supported and integrated by results coming from a numerical determination of the energy eigenvalues and eigenvectors of the off-critical systems in an infinite cylinder.Comment: 61 pages, Latex file, figures in a separate fil

2004 Presidential Election: Who Won The Popular Vote? An Examination of the Comparative Validity of Exit Poll and Vote Count Data

* There is a substantial discrepancy -- well outside the margin of error and outcomedeterminative -- between the national exit poll and the popular vote count.* The possible causes of the discrepancy would be random error, a skewed exit poll, or breakdown in the fairness of the voting process and accuracy of the vote count.* Analysis shows that the discrepancy cannot reasonably be accounted for by chance or random error.* Evidence does not support hypotheses that the discrepancy was produced by problems with the exit poll.* Widespread breakdown in the fairness of the voting process and accuracy of the vote count are the most likely explanations for the discrepancy.* In an accurate count of a free and fair election, the strong likelihood is that Kerry would have been the winner of the popular vote.This document was originally published by Verified Vote 2004, and is authored by Jonathan Simon, currently with Election Defense Alliance

Simulating star formation in molecular cloud cores I. The influence of low levels of turbulence on fragmentation and multiplicity

We present the results of an ensemble of simulations of the collapse and fragmentation of dense star-forming cores. We show that even with very low levels of turbulence the outcome is usually a binary, or higher-order multiple, system. We take as the initial conditions for these simulations a typical low-mass core, based on the average properties of a large sample of observed cores. All the simulated cores start with a mass of $M = 5.4 M_{\odot}$, a flattened central density profile, a ratio of thermal to gravitational energy $\alpha_{\rm therm} = 0.45$ and a ratio of turbulent to gravitational energy $\alpha_{\rm turb} = 0.05$. Even this low level of turbulence is sufficient to produce multiple star formation in 80% of the cores; the mean number of stars and brown dwarfs formed from a single core is 4.55, and the maximum is 10. At the outset, the cores have no large-scale rotation. The only difference between each individual simulation is the detailed structure of the turbulent velocity field. The multiple systems formed in the simulations have properties consistent with observed multiple systems. Dynamical evolution tends preferentially to eject lower mass stars and brown dwarves whilst hardening the remaining binaries so that the median semi-major axis of binaries formed is $\sim 30$ au. Ejected objects are usually single low-mass stars and brown dwarfs, yielding a strong correlation between mass and multiplicity. Our simulations suggest a natural mechanism for forming binary stars that does not require large-scale rotation, capture, or large amounts of turbulence.Comment: 20 pages, 12 figures submitted to A&

Quantum Computing: Pro and Con

I assess the potential of quantum computation. Broad and important applications must be found to justify construction of a quantum computer; I review some of the known quantum algorithms and consider the prospects for finding new ones. Quantum computers are notoriously susceptible to making errors; I discuss recently developed fault-tolerant procedures that enable a quantum computer with noisy gates to perform reliably. Quantum computing hardware is still in its infancy; I comment on the specifications that should be met by future hardware. Over the past few years, work on quantum computation has erected a new classification of computational complexity, has generated profound insights into the nature of decoherence, and has stimulated the formulation of new techniques in high-precision experimental physics. A broad interdisciplinary effort will be needed if quantum computers are to fulfill their destiny as the world's fastest computing devices. (This paper is an expanded version of remarks that were prepared for a panel discussion at the ITP Conference on Quantum Coherence and Decoherence, 17 December 1996.)Comment: 17 pages, LaTeX, submitted to Proc. Roy. Soc. Lond. A, minor correction

The construction of a reliable potential for GeO2 from first-principles

The construction of a reliable potential for GeO2, from first-principles, is described. The obtained potential, which includes dipole polarization effects, is able to reproduce all the studied properties (structural, dynamical and vibrational) to a high degree of precision with a single set of parameters. In particular, the infrared spectrum was obtained with the expression proposed for the dielectric function of polarizable ionic solutions by Weis et al. [J.M. Caillol, D. Levesque and J.J. Weis, J. Chem. Phys. 91, 5544 (1989)]. The agreement with the experimental spectrum is very good, with three main bands that are associated to tetrahedral modes of the GeO2 network. Finally, we give a comparison with a simpler pair-additive potential.Comment: 9 pages, 8 figure

Evidence for a continuum limit in causal set dynamics

We find evidence for a continuum limit of a particular causal set dynamics which depends on only a single ``coupling constant'' $p$ and is easy to simulate on a computer. The model in question is a stochastic process that can also be interpreted as 1-dimensional directed percolation, or in terms of random graphs.Comment: 24 pages, 19 figures, LaTeX, adjusted terminolog