  We present a theoretical and numerical study of the competition between two
opposite interference effects, namely interference-induced ballistic transport
on one hand, and strong (Anderson) localization on the other. While the former
effect allows for resistance free transport, the latter brings the transport to
a complete halt. As a model system, we consider the quantum kicked rotor, where
strong localization is observed in the discrete momentum coordinate. In this
model, we introduce the ballistic transport in the form of a Hadamard quantum
walk in that momentum coordinate. The two transport mechanisms are combined by
alternating the corresponding Floquet operators. Extending the corresponding
calculation for the kicked rotor, we estimate the classical diffusion
coefficient for thecombined dynamics. Another argument, based on the
introduction of an effective Heisenberg time should then allow to estimate the
localization time and the localization length. While this is known to work
reasonably 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 much
larger times and shows much larger localization lengths than predicted.
Finally, we combine the kicked rotor with other types of quantum walks, namely
diffusive and localizing quantum walks. In the diffusive case, the localizing
dynamics of the kicked rotor is completely canceled and we get pure diffusion.
In the case of the localizing quantum walk, the combined system remains
localized, but with a larger localization length.
