P. Exner, P. {\v S}eba, M. Tater, D. Van{\v e}k
Bound states and scattering in quantum waveguides
coupled laterally through a boundary window
(579K, LaTeX, ps figures)
ABSTRACT. We consider a pair of parallel straight quantum waveguides coupled
laterally through a window of a width $\,\ell\,$ in the common boundary.
We show that such a system has at least one bound state for any
$\,\ell>0\,$. We find the corresponding eigenvalues and eigenfunctions
numerically using the mode--matching method, and discuss their
behavior in several situations. We also discuss the scattering
problem in this setup, in particular, the turbulent behavior of the
probability flow associated with resonances. The level and
phase--shift spacing statistics shows that in distinction to closed
pseudo--integrable billiards, the present system is essentially
non--chaotic. Finally, we illustrate time evolution of wave packets
in the present model.