Discrete Dirac system: rectangular Weyl functions, direct and inverse problems

A transfer matrix function representation of the fundamental solution of the general-type discrete Dirac system, corresponding to rectangular Schur coefficients and Weyl functions, is obtained. Connections with Szeg\"o recurrence, Schur coefficients and structured matrices are treated. Borg-Marchenko-type uniqueness theorem is derived. Inverse problems on the interval and semiaxis are solved.Comment: Section 2 is improved in the second version: some new results on Halmos extension are added and arguments are simplifie

Reverse-domain superconductivity in superconductor-ferromagnet hybrids: effect of a vortex-free channel on the symmetry of I-V characteristics

We demonstrate experimentally that the presence of a single domain wall in an underlying ferromagnetic BaFe_{12}O_{19} substrate can induce a considerable asymmetry in the current (I) - voltage (V) characteristics of a superconducting Al bridge. The observed diode-like effect, i.e. polarity-dependent critical current, is associated with the formation of a vortex-free channel inside the superconducting area which increases the total current flowing through the superconducting bridge without dissipation. The vortex-free region appears only for a certain sign of the injected current and for a limited range of the external magnetic field

Classical analogy for the deflection of flux avalanches by a metallic layer

Sudden avalanches of magnetic flux bursting into a superconducting sample undergo deflections of their trajectories when encountering a conductive layer deposited on top of the superconductor. Remarkably, in some cases flux is totally excluded from the area covered by the conductive layer. We present a simple classical model that accounts for this behaviour and considers a magnetic monopole approaching a semi-infinite conductive plane. This model suggests that magnetic braking is an important mechanism responsible for avalanche deflection.Comment: 14 pages, 5 figure