Kink propagation in a two-dimensional curved Josephson junction

We consider the propagation of sine-Gordon kinks in a planar curved strip as a model of nonlinear wave propagation in curved wave guides. The homogeneous Neumann transverse boundary conditions, in the curvilinear coordinates, allow to assume a homogeneous kink solution. Using a simple collective variable approach based on the kink coordinate, we show that curved regions act as potential barriers for the wave and determine the threshold velocity for the kink to cross. The analysis is confirmed by numerical solution of the 2D sine-Gordon equation.Comment: 8 pages, 4 figures (2 in color

Conductance distribution between Hall plateaus

Mesoscopic fluctuations of two-port conductance and four-port resistance between Hall plateaus are studied within a realistic model for a two-dimensional electron gas in a perpendicular magnetic field and a smooth disordered potential. The two-port conductance distribution $P(g)$ is concave between $g=0$ and $g=1$ and is nearly flat between $g=0.2$ and $g=0.8$. These characteristics are consistent with recent observations. The distribution is found to be sharply peaked near the end-points $g=0$ and $g=1$. The distribution functions for the three independent resistances in a four-port Hall bar geometry are, on the other hand, characterized by a central peak and a relatively large width.Comment: 11 pages, 5 ps figures, submitted to Phys. Rev.

Multiple bound states in scissor-shaped waveguides

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.Comment: 6 pages, 6 figure

Effective one-dimensional square well for two-dimensional quantum wires

The symmetrical two-dimensional quantum wire with two straight leads joined to an arbitrarily shaped interior cavity is studied with emphasis on the single-mode approximation. It is found that for both transmission and bound-state problems the solution is equivalent to that for an energy-dependent one-dimensional square well. Quantum wires with a circular bend, and with single and double right-angle bends, are examined as examples. We also indicate a possible way to detect bound states in a double bend based on the experimental setup of Wu et al