4,030,095 research outputs found

    Inverse problem for an inhomogeneous Schr\"odinger equation

    Get PDF
    An inverse problem is considered for an inhomogeneous Schr\"odinger equation. Assuming that the potential vanishes outside a finite interval and satisfies some other technical assumptions, one proves the uniqueness of the recovery of this potential from the knowledge of the wave function at the ends of the above interval for all energies. An algorithm is given for the recovery of the potential from the above data

    Global well-posedness and scattering for the defocusing energy-critical nonlinear Schr\"odinger equation in R1+4\R^{1+4}

    Full text link
    We obtain global well-posedness, scattering, uniform regularity, and global Lt,x6L^6_{t,x} spacetime bounds for energy-space solutions to the defocusing energy-critical nonlinear Schr\"odinger equation in R×R4\R\times\R^4. Our arguments closely follow those of Colliander-Keel-Staffilani-Takaoka-Tao, though our derivation of the frequency-localized interaction Morawetz estimate is somewhat simpler. As a consequence, our method yields a better bound on the Lt,x6L^6_{t,x}-norm

    PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation

    Get PDF
    We discuss several PT-symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT-symmetric deformations of the supersymmetric Korteweg-de Vries equation. Some of these new models are mere fermionic extensions of the former in the sense that they are formulated in terms of superspace valued superfields containing bosonic and fermionic fields, breaking however the supersymmetry invariance. Nonetheless, we also find extensions, which may be viewed as new supersymmetric Korteweg-de Vries equation. Moreover, we show that these deformations allow for a non-Hermitian Hamiltonian formulation and construct three charges associated to the corresponding flow.Comment: 10 page

    Discrete--time ratchets, the Fokker--Planck equation and Parrondo's paradox

    Get PDF
    Parrondo's games manifest the apparent paradox where losing strategies can be combined to win and have generated significant multidisciplinary interest in the literature. Here we review two recent approaches, based on the Fokker-Planck equation, that rigorously establish the connection between Parrondo's games and a physical model known as the flashing Brownian ratchet. This gives rise to a new set of Parrondo's games, of which the original games are a special case. For the first time, we perform a complete analysis of the new games via a discrete-time Markov chain (DTMC) analysis, producing winning rate equations and an exploration of the parameter space where the paradoxical behaviour occurs.Comment: 17 pages, 5 figure
    • …
    corecore