  The classical drift diffusion (DD) model of spin transport treats spin
relaxation via an empirical parameter known as the ``spin diffusion length''.
According to this model, the ensemble averaged spin of electrons drifting and
diffusing in a solid decays exponentially with distance due to spin dephasing
interactions. The characteristic length scale associated with this decay is the
spin diffusion length. The DD model also predicts that this length is different
for ``upstream'' electrons traveling in a decelerating electric field than for
``downstream'' electrons traveling in an accelerating field. However this
picture ignores energy quantization in confined systems (e.g. quantum wires)
and therefore fails to capture the non-trivial influence of subband structure
on spin relaxation. Here we highlight this influence by simulating upstream
spin transport in a multi-subband quantum wire, in the presence of
D'yakonov-Perel' spin relaxation, using a semi-classical model that accounts
for the subband structure rigorously. We find that upstream spin transport has
a complex dynamics that defies the simplistic definition of a ``spin diffusion
length''. In fact, spin does not decay exponentially or even monotonically with
distance, and the drift diffusion picture fails to explain the qualitative
behavior, let alone predict quantitative features accurately. Unrelated to spin
transport, we also find that upstream electrons undergo a ``population
inversion'' as a consequence of the energy dependence of the density of states
in a quasi one-dimensional structure.
