  Recent studies of transport phenomena with complex potentials are explained
by generic square root singularities of spectrum and eigenfunctions of
non-Hermitian Hamiltonians. Using a two channel problem we demonstrate that
such singularities produce a significant effect upon the pole behaviour of the
scattering matrix, and more significantly upon the associated residues. This
mechanism explains why by proper choice of the system parameters the resonance
cross section is increased drastically in one channel and suppressed in the
other channel.
