  Entanglement production in coupled chaotic systems is studied with the help
of kicked tops. Deriving the correct classical map, we have used the reduced
Husimi function, the Husimi function of the reduced density matrix, to
visualize the possible behaviors of a wavepacket. We have studied a phase space
based measure of the complexity of a state and used random matrix theory (RMT)
to model the strongly chaotic cases. Extensive numerical studies have been done
for the entanglement production in coupled kicked tops corresponding to
different underlying classical dynamics and different coupling strengths. An
approximate formula, based on RMT, is derived for the entanglement production
in coupled strongly chaotic systems. This formula, applicable for arbitrary
coupling strengths and also valid for long time, complements and extends
significantly recent perturbation theories for strongly chaotic weakly coupled
systems.
