  An environment interacting with a quantum system can enhance transport
through the suppression of quantum effects responsible for localization. In
this paper, we study the interplay between bulk dephasing and a linear
potential in a boundary-driven tight-binding chain. A linear potential induces
Wannier-Stark localization in the absence of noise, while dephasing induces
diffusive transport in the absence of a tilt. We derive an approximate
expression for the steady-state current as a function of both dephasing and
tilt which closely matches the exact solution for a wide range of parameters.
From it, we find that the maximum current occurs for a dephasing rate equal to
the period of Bloch oscillations in the Wannier-Stark localized system. We also
find that the current displays a maximum as a function of the system size,
provided that the total potential tilt across the chain remains constant. Our
results can be verified in current experimental platforms and represents a step
forward in analytical studies of environment-assisted transport.
