We examine the time evolution of the nonlinear propagation of a partic
le or excitation in strong interaction with vibrations. We carry out c
alculations for the density matrix elements of the quantum nonlinear d
imer without imposing the adiabatic limit. In contrast to earlier anal
yses which have treated the problem in the limit of extremely large or
moderately large dissipation, i.e., respectively, the cases of infini
te damping and severe overdamping, we investigate the case of no dissi
pation. Exact solutions are obtained for a restricted range of paramet
ers. We exhibit the existence of the transition between a localized an
d delocalized state of the dimer, known from the adiabatic case. Simil
ar behavior is observed in (numerically obtained) solutions valid outs
ide the parameter range where analytical solutions can be obtained. Th
e study is of direct interest in the context of any two-state quantum
mechanical system interacting with a boson field, such as photons (lig
ht) or phonons (vibrations of a solid) whenever the boson field can be
treated classically