  In this Letter, we investigate the effects of a time-dependent, short-ranged
interaction on the long-time expansion dynamics of Fermi gases. We show that
the effects of the interaction on the dynamics is dictated by how it changes
under a conformal transformation, and derive an explicit criterion for the
relevancy of time-dependent interactions in both the strongly and
non-interacting nearly scale invariant quantum gases. In addition, we show that
it is possible to engineer interactions that give rise to non-exponential
thermalization dynamics in trapped Fermi gases. To supplement the symmetry
analysis, we also perform hydrodynamic simulations to show that the moment of
inertia of the trapped gas indeed follows a universal time-dependence
determined jointly by the conformal symmetry and time-dependent scattering
length $a(t)$. Our results should also be relevant to the dynamics of other
systems that are nearly scale invariant and that are governed by a
non-relativistic conformal symmetry.
