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 $Ntoinfty$, 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 $Ngeq 2$ 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.
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