Solvable Quantum‐Mechanical Model of Three‐Body Rearrangement Scattering

Theory of a curved planar waveguide with Robin boundary conditions

A model of a thin straight strip with a uniformly curved section and with boundary requirements zeroing at the edges a linear superposition of the wave function and its normal derivative (Robin boundary condition) is analyzed theoretically within the framework of the linear Schrödinger equation and is applied to the study of the processes in the bent magnetic multilayers, superconducting films and metallic ferrite-filled waveguides. In particular, subband thresholds of the straight and curved parts of the film are calculated and analyzed as a function of the Robin parameter 1/Lambda , with Lambda being an extrapolation length entering Robin boundary condition. For the arbitrary Robin coefficients which are equal on the opposite interfaces of the strip and for all bend parameters the lowest-mode energy of the continuously curved duct is always smaller than its straight counterpart. Accordingly, the bound state below the fundamental propagation threshold of the straight arms always exists as a result of the bend. In terms of the superconductivity language it means an increased critical temperature of the curved film compared to its straight counterpart. Localized-level dependence on the parameters of the curve is investigated with its energy decreasing with increasing bend angle and decreasing bend radius. Conditions of the bound-state existence for the different Robin parameters on the opposite edges are analyzed too; in particular, it is shown that the bound state below the first transverse threshold of the straight arm always exists if the inner extrapolation length is not larger than the outer one. In the opposite case there is a range of the bend parameters where the curved film cannot trap the wave and form the localized mode; for example, for the fixed bend radius the bound state emerges from the continuum at some nonzero bend angle that depends on the difference of the two lengths Lambda at the opposite interfaces. Various transport properties of the film such as interference blockade of the current flow at some special energies is also discussed with the special attention being paid to the transformation from the Dirichlet to the Neumann case as the extrapolation length Lambda sweeps the positive axis.

Localized-mode evolution in a curved planar waveguide with combined Dirichlet and Neumann boundary conditions

We present a theoretical study of a planar waveguide with a uniformly curved section. Opposite sides of the channel satisfy different boundary conditions. It is shown that if the Dirichlet condition is applied to the inner side of the strip and the Neumann one to the outer wall, then properties of such a system in many respects resemble those with the Dirichlet requirements on both surfaces. Namely, in both cases a propagation threshold for the curved section is smaller than its counterpart for the straight channel. As a consequence, a localized mode exists with its energy below the propagation threshold of the straight waveguide. Analysis of such states is presented as a function of the bend parameters. For the transport in the fundamental mode an interaction of a quasibound level split off from the higher-lying threshold, with its degenerate continuum counterpart, causes a dip in the transmission. Such a resonance is characterized by a location of its zero minimum E(min) and the half width Gamma. Changing the bend angle and radius, one varies E(min) and Gamma. In particular, for some critical parameters of the bend it is possible to turn the half width to zero, i.e., to eliminate the dip in the transmission. This corresponds to the absence of the interaction between the split-off level and the continuum, and, consequently, to the formation of the true bound state in the continuum. Vortex structure of the currents flowing in the waveguide near the resonance is also shown to strongly resemble the analogous results for the Dirichlet case. It is pointed out that the properties of the waveguide with the Neumann inner condition and the Dirichlet outer one mimic the duct with the Neumann requirements on the two sides, since for both these cases the propagation threshold in the curved section is greater than in the straight channel.