1 research outputs found
Quantum waveguides with a lateral semitransparent barrier: spectral and scattering properties
We consider a quantum particle in a waveguide which consists of an infinite
straight Dirichlet strip divided by a thin semitransparent barrier on a line
parallel to the walls which is modeled by a potential. We show that if
the coupling strength of the latter is modified locally, i.e. it reaches the
same asymptotic value in both directions along the line, there is always a
bound state below the bottom of the essential spectrum provided the effective
coupling function is attractive in the mean. The eigenvalues and
eigenfunctions, as well as the scattering matrix for energies above the
threshold, are found numerically by the mode-matching technique. In particular,
we discuss the rate at which the ground-state energy emerges from the continuum
and properties of the nodal lines. Finally, we investigate a system with a
modified geometry: an infinite cylindrical surface threaded by a homogeneous
magnetic field parallel to the cylinder axis. The motion on the cylinder is
again constrained by a semitransparent barrier imposed on a ``seam'' parallel
to the axis.Comment: a LaTeX source file with 12 figures (11 of them eps); to appear in J.
Phys. A: Math. Gen. Figures 3, 5, 8, 9, 11 are given at 300 dpi; higher
resolution originals are available from the author