  Spin propagation in systems of one-dimensional interacting fermions at finite
temperature is intrinsically diffusive. The spreading rate of a spin packet is
controlled by a transport coefficient termed "spin drag" relaxation time
$\tau_{\rm sd}$. In this paper we present both numerical and analytical
calculations of $\tau_{\rm sd}$ for a two-component spin-polarized cold Fermi
gas trapped inside a tight atomic waveguide. At low temperatures we find an
activation law for $\tau_{\rm sd}$, in agreement with earlier calculations of
Coulomb drag between slightly asymmetric quantum wires, but with a different
and much stronger temperature dependence of the prefactor. Our results provide
a fundamental input for microscopic time-dependent spin-density functional
theory calculations of spin transport in 1D inhomogeneous systems of
interacting fermions.
