  On the basis of the two-site polaron problem, which we solve by exact
diagonalization, we analyse the spectral properties of polaronic systems in
view of discerning localized from itinerant polarons and bound polaron pairs
from an ensemble of single polarons. The corresponding experimental techniques
for that concern photoemission and inverse photoemission spectroscopy. The
evolution of the density of states as a function of concentration of charge
carriers and strength of the electron-phonon interaction clearly shows the
opening up of a gap between single polaronic and bi-polaronic states, in
analogy to the Hubbard problem for strongly correlated electron systems. The
crossover regime between adiabatic and anti-adiabatic small polarons is
triggered by two characteristic time scales: the renormalized electron hopping
rate and the renormalized vibrational frequency becoming equal. This crossover
regime is then characterized by temporarily alternating self- localization and
delocalization of the charge carriers which is accompanied by phase slips in
the charge and molecular deformation oscillations and ultimately leads to a
dephasing between these two dynamical components of the polaron problem. We
visualize these features by a study of the temporal evolution of the charge
redistribution and the change in molecular deformations. The spectral and
dynamical properties of polarons discussed here are beyond the applicability of
the standard Lang Firsov approach to the polaron problem.
