52,163 research outputs found

    Josephson junction on one edge of a two dimensional topological insulator affected by magnetic impurity

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    Current-phase relation in a Josephson junction formed by putting two s-wave superconductors on the same edge of a two dimensional topological insulator is investigated. We consider the case that the junction length is finite and magnetic impurity exists. The similarity and difference with conventional Josephson junction is discussed. The current is calculated in the semiconductor picture. Both the 2π2\pi- and 4π4\pi-period current-phase relations (I2π(ϕ),I4π(ϕ)I_{2\pi}(\phi), I_{4\pi}(\phi)) are studied. There is a sharp jump at ϕ=π\phi=\pi and ϕ=2π\phi=2\pi for I2πI_{2\pi} and I4πI_{4\pi} respectively in the clean junction. For I2πI_{2\pi}, the sharp jump is robust against impurity strength and distribution. However for I4πI_{4\pi}, the impurity makes the jump at ϕ=2π\phi=2\pi smooth. The critical (maximum) current of I2πI_{2\pi} is given and we find it will be increased by asymmetrical distribution of impurity.Comment: 7 pages, 5 figure

    What is the Impact of Software Patent Shifts?: Evidence from Lotus v. Borland

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    Economists have debated the extent to which strengthening patent protection spurs or detracts from technological innovation. In this paper, we examine the reduction of software copyright protection in the Lotus v. Borland decision. If patent and copyright protections are substitutes, then weakening of one form of protection should be associated with an increasing reliance on the other. We find that the firms affected by the diminution of copyright protection disproportionately accelerated their patenting in subsequent years. But little evidence can be found for harmful effects: in fact, the increased reliance on patents is correlated with some positive outcomes for firms.

    Metapopulation Dynamics with Migration and Local Competition

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    MSC2000: primary 34D15, 34D23, 92B05; secondary 34K60, 34E13, 92D40.Many patch-based metapopulation models assume that the local population within each patch is at its equilibrium and independent of changes in patch occupancy. We study a metapopulation model which explicitly incorporates the local population dynamics of two competing species. Singular perturbation method is used to separate the fast dynamics of the local competition and the slow process of patch colonization and extinction. Our results show that the coupled system leads to much more complex outcomes than simple patch models that do not include explicit local dynamics.The first author was partially supported by NSF grant DMS-9974389 and NSF grant ESE-0119908. The second author was partially supported by NSF grant DMS-9803581. The third author was partially supported by a Canadian NSERC postdoctoral fellowship

    Detecting Gravitational Waves by Twisted Light - Dipole Interaction of Photons and Gravitational Waves

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    Motivated by the next generation of gravitational wave (GW) detectors, we study the wave mechanics of a twisted light beam in the GW perturbed spacetime. We found a new gravitational dipole interaction of photons and gravitational waves. Physically, this interaction is due to coupling between the angular momentum of twisted light and the GW polarizations. We demonstrate that for the higher-order Laguerre-Gauss (LG) modes, this coupling effect makes photons undergoing dipole transitions between different orbital-angular-momentum(OAM) eigenstates, and leads to some measurable optical features in the 2-D intensity pattern. It offers an alternative way to realize precision measurements of the gravitational waves, and enables us to extract more information about the physical properties of gravitational waves than the current interferometry. With a well-designed optical setup, this dipole interaction is expected to be justified in laboratories.Comment: 4 pages, 2 figure