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We present a theoretical and numerical study of the competition between twoopposite interference effects, namely interference-induced ballistic transporton one hand, and strong (Anderson) localization on the other. While the formereffect allows for resistance free transport, the latter brings the transport toa complete halt. As a model system, we consider the quantum kicked rotor, wherestrong localization is observed in the discrete momentum coordinate. In thismodel, we introduce the ballistic transport in the form of a Hadamard quantumwalk in that momentum coordinate. The two transport mechanisms are combined byalternating the corresponding Floquet operators. Extending the correspondingcalculation for the kicked rotor, we estimate the classical diffusioncoefficient for thecombined dynamics. Another argument, based on theintroduction of an effective Heisenberg time should then allow to estimate thelocalization time and the localization length. While this is known to workreasonably well in the kicked rotor case, we find that it fails in our case.While the combined dynamics still shows localization, it takes place at muchlarger times and shows much larger localization lengths than predicted.Finally, we combine the kicked rotor with other types of quantum walks, namelydiffusive and localizing quantum walks. In the diffusive case, the localizingdynamics of the kicked rotor is completely canceled and we get pure diffusion.In the case of the localizing quantum walk, the combined system remainslocalized, but with a larger localization length.

Quantum transport in a combined kicked rotor and quantum walk system