  We investigate dynamical many-body localization and delocalization in an
integrable system of periodically-kicked, interacting linear rotors. The
Hamiltonian we investigate is linear in momentum, and its Floquet evolution
operator is analytically tractable for arbitrary interaction strengths. One of
the hallmarks of this model is that depending on certain parameters, it
manifest both localization and delocalization in momentum space. We explicitly
show that for this model, the energy being bounded at long times is not a
sufficient condition for dynamical localization. Besides integrals of motion
associated to the integrability, this model manifests additional integrals of
motion, which are the exclusive consequence of dynamical many-body
localization. We also propose an experimental scheme, involving voltage-biased
Josephson junctions, to realize such many-body kicked models.
