  For harmonic-trapped atomic systems, we report system-independent
non-adiabatic features in the response to interaction ramps. We provide results
for several different systems in one, two, and three dimensions: bosonic and
fermionic Hubbard models realized through optical lattices, a Bose-Einstein
condensate, a fermionic superfluid and a fermi liquid. The deviation from
adiabaticity is characterized through the heating or excitation energy produced
during the ramp. We find that the dependence of the heat on the ramp time is
sensitive to the ramp protocol but has aspects common to all systems
considered. We explain these common features in terms of universal dynamics of
the system size or cloud radius.
