  Despite the periodic kicks, a linear kicked rotor (LKR) is an integrable and
exactly solvable model in which the kinetic energy term is linear in momentum.
It was recently shown that spatially interacting LKRs are also integrable, and
results in dynamical localization in the corresponding quantum regime. Similar
localized phases exist in other non-integrable models such as the coupled
relativistic kicked rotors. This work, using a two-body LKR, demonstrates two
main results; firstly, it is shown that chaos can be induced in the integrable
linear kicked rotor through interactions between the momenta of rotors. An
analytical estimate of its Lyapunov exponent is obtained. Secondly, the quantum
dynamics of this chaotic model, upon variation of kicking and interaction
strengths, is shown to exhibit a variety of phases -- classically induced
localization, dynamical localization, subdiffusive and diffusive phases. We
point out the signatures of these phases from the perspective of entanglement
production in this system. By defining an effective Hilbert space dimension,
the entanglement growth rate can be understood using appropriate random matrix
averages.
