  We study spin transport in a one-dimensional finite-length wire connected to
fermionic leads. The interacting wire is described by the sine-Gordon model
while the leads are either noninteracting or interacting Luttinger liquids. We
calculate the spin current driven by a spin bias by solving numerically the
classical equation of motion, and we find that the cosine term in the
sine-Gordon model gives rise to an oscillating spin current when the spin bias
exceeds its critical value. We discuss the results in connection with transport
experiments with ultracold atoms.
