  A charge motion in an electric field in a Holstein molecular chain is modeled
in the absence of dissipation. It is shown that in a weak electric field a
Holstein polaron moves uniformly experiencing small oscillations of its shape.
These oscillations are associated with the chain's discreteness and caused by
the presence of Peierls-Nabarro potential there. The critical value of the
electric field intensity at which the moving polaron starts oscillating at
Bloch frequency is found. It is shown that the polaron can demonstrate Bloch
oscillations retaining its shape. It is also shown that a breathing mode of
Bloch oscillations can arise. In all cases the polaron motion along the chain
is infinite.
