  When a free Fermi gas on a lattice is subject to the action of a linear
potential it does not drift away, as one would naively expect, but it remains
spatially localized. Here we revisit this phenomenon, known as Stark
localization, within the recently proposed framework of generalized
hydrodynamics. In particular, we consider the dynamics of an initial state in
the form of a domain wall and we recover known results for the particle density
and the particle current, while we derive analytical predictions for relevant
observables such as the entanglement entropy and the full counting statistics.
Then, we extend the analysis to generic potentials, highlighting the
relationship between the occurrence of localization and the presence of
peculiar closed orbits in phase space, arising from the lattice dispersion
relation. We also compare our analytical predictions with numerical
calculations and with the available results, finding perfect agreement. This
approach paves the way for an exact treatment of the interacting case known as
Stark many-body localization.
