Diffusion and thermalization in a boundary-driven dephasing model

We study a model of non-interacting spinless fermions coupled to local dephasing and boundary drive described within Lindblad master equation. The features an interplay between infinite temperature thermalization due bulk non-equilibrium stationary state the dissipation. revisit linear non-linear transport properties model, featuring crossover from ballistic diffusive scaling, compute spectral occupation encoded in single particle Green's functions, that we exactly using equations motion spite \emph{interacting} nature term. show distribution function system becomes frequency independent flat, consistent with thermalization, while near boundaries it retains strong reflect continuous injection depletion particles driving