  We study the effect of many-body quantum interference on the dynamics of
coupled periodically kicked systems whose classical dynamics is chaotic and
shows an unbounded energy increase. We specifically focus on a $N$ coupled
kicked rotors model: we find that the interplay of quantumness and interactions
dramatically modifies the system dynamics inducing a transition between energy
saturation and unbounded energy increase. We discuss this phenomenon both
numerically and analytically, through a mapping onto a $N$-dimensional Anderson
model. The thermodynamic limit $N\to\infty$, in particular, always shows
unbounded energy growth. This dynamical delocalization is genuinely quantum and
very different from the classical one: using a mean field approximation we see
that the system self-organizes so that the energy per site increases in time as
a power law with exponent smaller than one. This wealth of phenomena is a
genuine effect of quantum interference: the classical system for $N\geq 2$
always behaves ergodically with an energy per site linearly increasing in time.
Our results show that quantum mechanics can deeply alter the
regularity/ergodicity properties of a many body driven system.
