  Nonhermitean hamiltonians of convection-diffusion type occur in the
description of vortex motion in the presence of a tilted magnetic field as well
as in models of driven population dynamics. We study such hamiltonians in the
case of rectangular barriers of variable size. We determine Lyapunov exponent
and wavenumber of the eigenfunctions within an adiabatic approach, allowing to
reduce the original d=2 phase space to a d=1 attractor. PACS
numbers:05.70.Ln,72.15Rn,74.60.Ge
