  We map the infinite-range coupled quantum kicked rotors over an
infinite-range coupled interacting bosonic model. In this way we can apply
exact diagonalization up to quite large system sizes and confirm that the
system tends to ergodicity in the large-size limit. In the thermodynamic limit
the system is described by a set of coupled Gross-Pitaevskij equations
equivalent to an effective nonlinear single-rotor Hamiltonian. These equations
give rise to a power-law increase in time of the energy with exponent
$\gamma\sim 2/3$ in a wide range of parameters. We explain this finding by
means of a master-equation approach based on the noisy behaviour of the
effective nonlinear single-rotor Hamiltonian and on the Anderson localization
of the single-rotor Floquet states. Furthermore, we study chaos by means of the
largest Lyapunov exponent and find that it decreases towards zero for portions
of the phase space with increasing momentum. Finally, we show that some
stroboscopic Floquet integrals of motion of the noninteracting dynamics deviate
from their initial values over a time scale related to the interaction strength
according to the Nekhoroshev theorem.
