  We investigate the mean field regime of the dynamics of a tracer particle in
a homogenous quantum gas. For a bosonic gas, we show that this regime is
constrained by the well known requirement of an appropriate mean field scaling
of the interaction. For fermions, however, we find an important qualitative
difference. Not only are fermions much more homogeneously distributed than
bosons but also deviations from the mean are due only to fast degrees of
freedom in the gas. This observation leads to an explanation of why a tracer
particle behaves freely in the dense homogeneous fermion gas despite of a
non-scaled interaction, i.e., despite of non-vanishing statistical
fluctuations. Finally, we indicate how the gained insight can be rigorously
justified.
