  The behavior of the 1D Holstein polaron is described, with emphasis on
lattice coarsening effects, by distinguishing between adiabatic and
nonadiabatic contributions to the local correlations and dispersion properties.
The original and unifying systematization of the crossovers between the
different polaron behaviors, usually considered in the literature, is obtained
in terms of quantum to classical, weak coupling to strong coupling, adiabatic
to nonadiabatic, itinerant to self-trapped polarons and large to small
polarons. It is argued that the relationship between various aspects of polaron
states can be specified by five regimes: the weak-coupling regime, the regime
of large adiabatic polarons, the regime of small adiabatic polarons, the regime
of small nonadiabatic (Lang-Firsov) polarons, and the transitory regime of
small pinned polarons for which the adiabatic and nonadiabatic contributions
are inextricably mixed in the polaron dispersion properties. The crossovers
between these five regimes are positioned in the parameter space of the
Holstein Hamiltonian.
