Selective Equal-Spin Andreev Reflections Induced by Majorana Fermions

In this work, we find that Majorana fermions induce selective equal spin Andreev reflections (SESARs), in which incoming electrons with certain spin polarization in the lead are reflected as counter propagating holes with the same spin. The spin polarization direction of the electrons of this Andreev reflected channel is selected by the Majorana fermions. Moreover, electrons with opposite spin polarization are always reflected as electrons with unchanged spin. As a result, the charge current in the lead is spin-polarized. Therefore, a topological superconductor which supports Majorana fermions can be used as a novel device to create fully spin-polarized currents in paramagnetic leads. We point out that SESARs can also be used to detect Majorana fermions in topological superconductors.Comment: 5 pages, 3 figures. Comments are welcome. Title changed to match published versio

Robustness of Majorana Fermion induced Fractional Josephson Effect

It is shown in previous works that the coupling between two Majorana end states in superconducting quantum wires leads to fractional Josephson effect. However, in realistic experimental conditions, multiple bands of the wires are occupied and the Majorana end states are accompanied by other fermionic end states. This raises the question concerning the robustness of fractional Josephson effect in these situations. In this work, we show that the absence of the avoided energy crossing which gives rise to the fractional Josephson effect is robust, even when the Majorana fermions are coupled with arbitrary strengths to other fermions. Moreover, we calculate the temperature dependence of the fractional Josephson current and show that it is suppressed by thermal excitations to the other fermion bound states.Comment: 4+ pages, 3 figure

Probing Non-Abelian Statistics in nu=12/5 Quantum Hall State

The tunneling current and shot noise of the current between two Fractional Quantum Hall (FQH) edges in the $\nu=12/5$ FQH state in electronic Mach-Zehnder interferometer are studied. It is shown that the tunneling current and shot noise can be used to probe the existence of $k=3$ parafermion statistics in the $\nu=12/5$ FQH state. More specifically, the dependence of the current on the Aharonov-Bohm flux in the Read-Rezayi state is asymmetric under the change of the sign of the applied voltage. This property is absent in the Abelian Laughlin states. Moreover the Fano factor can exceed 12.7 electron charges in the $\nu=12/5$ FQH state . This number well exceeds the maximum possible Fano factor in all Laughlin states and the $\nu=5/2$ Moore-Read state which was shown previously to be $e$ and $3.2 e$ respectively.Comment: 10 pages, 6 figure

Well-Posedness And Accuracy Of The Ensemble Kalman Filter In Discrete And Continuous Time

The ensemble Kalman filter (EnKF) is a method for combining a dynamical model with data in a sequential fashion. Despite its widespread use, there has been little analysis of its theoretical properties. Many of the algorithmic innovations associated with the filter, which are required to make a useable algorithm in practice, are derived in an ad hoc fashion. The aim of this paper is to initiate the development of a systematic analysis of the EnKF, in particular to do so in the small ensemble size limit. The perspective is to view the method as a state estimator, and not as an algorithm which approximates the true filtering distribution. The perturbed observation version of the algorithm is studied, without and with variance inflation. Without variance inflation well-posedness of the filter is established; with variance inflation accuracy of the filter, with resepct to the true signal underlying the data, is established. The algorithm is considered in discrete time, and also for a continuous time limit arising when observations are frequent and subject to large noise. The underlying dynamical model, and assumptions about it, is sufficiently general to include the Lorenz '63 and '96 models, together with the incompressible Navier-Stokes equation on a two-dimensional torus. The analysis is limited to the case of complete observation of the signal with additive white noise. Numerical results are presented for the Navier-Stokes equation on a two-dimensional torus for both complete and partial observations of the signal with additive white noise

Incorporating remote visits into an outpatient clinic

Copyright @ 2009 Operational Research Society Ltd. This is a post-peer-review, pre-copyedit version of an article published in Journal of Simulation. The definitive publisher-authenticated version Eatock and Eldabi (2009), "Incorporating remote visits into an outpatient clinic", Journal of Simulation, 3, 179–188 is available online at the link below.Most telemedicine studies are concerned with either the technological or diagnostic comparisons, rather than assessing the impact on clinic management. This has attributed to the retrospective nature of the studies, with lack of data being the main cause for not using simulation for prospective analysis. This article demonstrates the use of simulation to assess the impact of prospective systems by utilising data generated from clinical trials. The example used here is the introduction of remote consultations into an outpatient's clinic. The article addresses the issues of using secondary data, in terms of the differences between the trial, the model and future reality. The result of running the simulation model show that exchanging the mode of service delivery does not improve patient wait times as expected, and that a protocol change in association with the introduction of remote visits is necessary to provide a substantial reduction in patient wait times

Two Dimensional Ising Superconductivity in Gated MoS2_{2}

The Zeeman effect, which is usually considered to be detrimental to superconductivity, can surprisingly protect the superconducting states created by gating a layered transition metal dichalcogenide. This effective Zeeman field, which is originated from intrinsic spin orbit coupling induced by breaking in-plane inversion symmetry, can reach nearly a hundred Tesla in magnitude. It strongly pins the spin orientation of the electrons to the out-of-plane directions and protects the superconductivity from being destroyed by an in-plane external magnetic field. In magnetotransport experiments of ionic-gate MoS$_{2}$ transistors, where gating prepares individual superconducting state with different carrier doping, we indeed observe a spin- protected superconductivity by measuring an in-plane critical field $\textit{B}$$_{c2}$ far beyond the Pauli paramagnetic limit. The gating-enhanced $\textit{B}$$_{c2}$ is more than an order of magnitude larger compared to the bulk superconducting phases where the effective Zeeman field is weakened by interlayer coupling. Our study gives the first experimental evidence of an Ising superconductor, in which spins of the pairing electrons are strongly pinned by an effective Zeeman field

Electronic Mach-Zehnder interferometer as a tool to probe fractional statistics

We study transport through an electronic Mach-Zehnder interferometer recently devised at the Weizmann Institute. We show that this device can be used to probe statistics of quasiparticles in the fractional quantum Hall regime. We calculate the tunneling current through the interferometer as the function of the Aharonov-Bohm flux, temperature and voltage bias, and demonstrate that its flux-dependent component is strongly sensitive to the statistics of tunneling quasiparticles. More specifically, the flux-dependent and flux-independent contributions to the current are related by a power law, the exponent being a function of the quasiparticle statistics.Comment: 22 pages; 8 figure

Practical Bayesian support vector regression for financial time series prediction and market condition change detection

Support vector regression (SVR) has long been proven to be a successful tool to predict financial time series. The core idea of this study is to outline an automated framework for achieving a faster and easier parameter selection process, and at the same time, generating useful prediction uncertainty estimates in order to effectively tackle flexible real-world financial time series prediction problems. A Bayesian approach to SVR is discussed, and implemented. It is found that the direct implementation of the probabilistic framework of Gao et al. returns unsatisfactory results in our experiments. A novel enhancement is proposed by adding a new kernel scaling parameter (Formula presented.) to overcome the difficulties encountered. In addition, the multi-armed bandit Bayesian optimization technique is applied to automate the parameter selection process. Our framework is then tested on financial time series of various asset classes (i.e. equity index, credit default swaps spread, bond yields, and commodity futures) to ensure its flexibility. It is shown that the generalization performance of this parameter selection process can reach or sometimes surpass the computationally expensive cross-validation procedure. An adaptive calibration process is also described to allow practical use of the prediction uncertainty estimates to assess the quality of predictions. It is shown that the machine-learning approach discussed in this study can be developed as a very useful pricing tool, and potentially a market condition change detector. A further extension is possible by taking the prediction uncertainties into consideration when building a financial portfolio