  The topological phases of periodically-driven, or Floquet systems, rely on a
perfectly periodic modulation of system parameters in time. Even the smallest
deviation from periodicity leads to decoherence, causing the boundary (end)
states to leak into the system's bulk. Here, we show that in one dimension this
decay of topologically protected end states depends fundamentally on the nature
of the bulk states: a dispersive bulk results in an exponential decay, while a
localized bulk slows the decay down to a diffusive process. The localization
can be due to disorder, which remarkably counteracts decoherence even when it
breaks the symmetry responsible for the topological protection. We derive this
result analytically, using a novel, discrete-time Floquet-Lindblad formalism
and confirm out findings with the help of numerical simulations. Our results
are particularly relevant for experiments, where disorder can be tailored to
protect Floquet topological phases from decoherence.
