THE NONADIABATIC NONLINEAR QUANTUM DIMER IN THE ABSENCE OF DISSIPATION - EXACT-SOLUTIONS

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