On the basis of the two-site polaron problem, which we solve by exact
diagonalization, we analyze the spectral properties of polaronic syste
ms in view of discerning localized from itinerant polarons and bound p
olaron pairs from an ensemble of single polarons. The corresponding ex
perimental techniques for that concern photoemission and inverse photo
emission spectroscopy. The evolution of the density of states as a fun
ction of concentration of charge carriers and strength of the electron
-phonon interaction clearly shows the opening up of a gap between sing
le-polaronic and bipolaronic states, in analogy to the Hubbard problem
for strongly correlated electron systems. In studying the details of
the intricately linked dynamics of the charge carriers and of the mole
cular deformations which surround them, we find that in general the dy
namical delocalization of the charge carriers helps to strengthen the
phase coherence for itinerant polaronic states, except for the crossov
er regime between adiabatic and antiadiabatic small polarons. The cros
sover between these two regimes is triggered by two characteristic tim
e scales: the renormalized electron hopping rate and the renormalized
vibrational frequency becoming equal. This crossover regime is then ch
aracterized by temporarily alternating self-localization and delocaliz
ation of the charge carriers which is accompanied by phase slips in th
e charge and molecular deformation oscillations and ultimately leads t
o a dephasing between these two dynamical components of the polaron pr
oblem. We visualize these features by a study of the temporal evolutio
n of the charge redistribution and the change in molecular deformation
s. The spectral and dynamical properties of polarons discussed here ar
e beyond the applicability of the standard Lang-Firsov approach to the
polaron problem.