  The non-equilibrium spin dynamics of a one-dimensional system of repulsively
interacting fermions is studied by means of density-matrix
renormalization-group simulations. We focus on the short-time decay of the
oscillation amplitudes of the centers of mass of spin-up and spin-down
fermions. Due to many-body effects, the decay is found to evolve from quadratic
to linear in time, and eventually back to quadratic as the strength of the
interaction increases. The characteristic rate of the decay increases linearly
with the strength of repulsion in the weak-coupling regime, while it is
inversely proportional to it in the strong-coupling regime. Our predictions can
be tested in experiments on tunable ultra-cold few-fermion systems in
one-dimensional traps.
