  We discuss properties of interacting spinless fermions in a tilted optical
lattice as modeled by Heisenberg spin chain in magnetic (or electric) field
changing linearly across the chain. The system shows genuine features of strong
localization for a sufficiently large tilt with distinct features different
from disorder induced localization. In particular, Stark many-body localization
is characterized in time dynamics by a linear increase of the entanglement
entropy followed by a saturation at a constant, time independent value -- both
the number (classical) and the configuration (quantum) entropies saturate to a
constant value. Similarly, the correlation with the initial state (the so
called imbalance) stabilizes at a constant value (modulo large fluctuations
coming from short time Bloch-type oscillations). The presence of an additional
harmonic potential profoundly affects the dynamics of the model -- its behavior
resembles standard MBL characteristics -- the logarithmic growth of the
entanglement entropy in particular. In that case, we find strong revival
phenomena associated with the manifold of equally spaced states, degenerate in
the absence of the harmonic potential.
