  We map the infinite-range coupled quantum kicked rotors over a 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
according to the Nekhoroshev theorem.
