  We study the recent Floquet-realisation of the Harper-Hofstadter model in a
gas of cold bosonic atoms. We study in detail the scattering processes in this
system in the weakly interacting regime due to the interplay of particle
interactions and the explicit time dependence of the Floquet states that lead
to band transitions and heating. We focus on the experimentally used parameters
and explicitly model the transverse confining direction. Based on transition
rates computed within the Floquet-Fermi golden rule we obtain band population
dynamics which are in agreement with the dynamics observed in experiment.
Finally, we discuss whether and how photon-assisted collisions that may be the
source heating and band population dynamics might be suppressed in the
experimental setup by appropriate design of the transverse confining potential.
The suppression of such processes will become increasingly important as the
experiments progress into simulating strongly interacting systems in the
presence of artificial gauge fields.
