We study quantum transport in a quasiperiodic Aubry-Andr\'e-Harper (AAH)
model induced by the coupling of the system to a Markovian heat bath. We find
that coupling the heat bath locally does not affect transport in the
delocalized and critical phases, while it induces logarithmic transport in the
localized phase. Increasing the number of coupled sites at the central region
introduces a transient diffusive regime, which crosses over to logarithmic
transport in the localized phase and in the delocalized regime to ballistic
transport. On the other hand, when the heat bath is coupled to equally spaced
sites of the system, we observe a crossover from ballistic and logarithmic
transport to diffusion in the delocalized and localized regimes, respectively.
We propose a classical master equation, which captures our numerical
observations for both coupling configurations on a qualitative level and for
some parameters, even on a quantitative level. Using the classical picture, we
show that the crossover to diffusion occurs at a time that increases
exponentially with the spacing between the coupled sites, and the resulting
diffusion constant decreases exponentially with the spacing.Comment: 11 pages, 7 fig