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We investigate entanglement growth for a pair of coupled kicked rotors. Forweak coupling, the growth of the entanglement entropy is found to be initiallylinear followed by a logarithmic growth. We calculate analytically the timeafter which the entanglement entropy changes its profile, and a good agreementwith the numerical result is found. We further show that the different regimesof entanglement growth are associated with different rates of energy growthdisplayed by a rotor. At a large time, energy grows diffusively, which ispreceded by an intermediate dynamical localization. The time-span ofintermediate dynamical localization decreases with increasing couplingstrength. We argue that the observed diffusive energy growth is the result ofone rotor acting as an environment to the other which destroys the coherence.We show that the decay of the coherence is initially exponential followed by apower-law.

Linear and logarithmic entanglement production in an interacting chaotic system