  Motivated by cold-atom experiments and a desire to understand
far-from-equilibrium quantum transport, we analytically study the dynamics of
spin helices in the one-dimensional $XX$ model. We use a Jordan-Wigner
transformation to map the spin chain onto a non-interacting Fermi gas with
simple equations of motion. The resulting dynamics are nontrivial, however, as
the spin-helix initial condition corresponds to a highly nonequilibrium
distribution of the fermions. We find a separation of timescales between the
in-plane and out-of-plane spin dynamics. We gain insights from analyzing the
case of a uniform spin chain and from a semiclassical model. One of our key
findings is that the spin correlation functions decay as $t^{-1/2}$ at long
time, in contrast to the experimentally observed exponential decay.
