  We analyze the spin transport through a finite-size one-dimensional
interacting wire connected to noninteracting leads. By combining
renormalization-group arguments with other analytic considerations such as the
memory function technique and instanton tunneling, we find the temperature
dependence of the spin conductance in different parameter regimes in terms of
interactions and the wire length. The temperature dependence is found to be
nonmonotonic. In particular, the system approaches perfect spin conductance at
zero temperature for both attractive and repulsive interactions, in contrast
with the static spin conductivity. We discuss the connection of our results to
recent experiments with ultracold atoms and compare the theoretical prediction
to experimental data in the parameter regime where temperature is the largest
energy scale.
