Pavel Exner and David Krejcirik
Quantum waveguides with a lateral semitransparent barrier:
spectral and scattering properties
(1304K, LaTeX 2e)
ABSTRACT. 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 $\delta$ 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.