  We investigate a normal metal -- superconductor (point) contact in the limit
where the number of conducting channels in the metallic wire is reduced to few
channels. As the effective Fermi energy drops below the gap energy, a
conducting band with a width twice the Fermi energy is formed. Depending on the
mode of operation, the conduction band can be further squeezed, leading to
various non-linear effects in the current-voltage characteristics such as
current saturation, a N-shaped negative differential resistance, bistability,
and hysteresis.
