  We uncover current-bias characteristics of superfluid-normal state junctions
with weakly-interacting Bose gases. It is shown that in the presence of a
chemical potential bias the characteristics can strongly be asymmetric for
origin. The salient feature that is absent in the fermionic counterpart arises
from a tunneling process associated with a condensate and a bosonic Andreev
reflection process. It turns out that such processes are intrinsically
nonlinear and therefore do not obey Ohm's law even at a low bias. In addition,
the remaining processes are found to obey Ohm's law and become dominant for
transport driven by a temperature bias.
