  In this work, we study the dynamics of an atomic harmonically trapped
large-spin Fermi gas in one dimension (1D). We investigate the interplay of
different collision processes. Coherent spin oscillations, driven by
spin-changing forward scattering are captured by a mean-field description and
scale linearly with density regardless of the dimension of the system.
Conversely, "incoherent" collision processes which e.g. lead to the damping of
spin oscillations, behave differently. In the usual three-dimensional (3D)
case, the rate of incoherent processes increases faster with density than
mean-field effects, but in 1D it increases slower. This means, that in the 1D
case, incoherent collisions become more important at lower densities. We study
these effects by deriving and integrating a quantum Boltzmann equation. We
demonstrate that the well known fact that in one dimension, interaction-induced
correlations become more dominant at low densities can be observed in
far-from-equilibrium spin dynamics.
