Time evolution of the nonadiabatic nonlinear quantum dimer

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Abstract
We analyze the set of coupled equations which describe the strong interactions between a moving quasiparticle in a solid and vibrations of the solid responsible for self-trapping and other polaronic and solitonic phenomena. The goal of the investigation is the examination of novel effects, if any, of relaxing the traditional (adiabaticity) assumption of disparate time scales for the quasiparticle motion and the vibrations. The study uncovers several striking phenomena including an approach to the self-trapped stationary states of the adiabatic dimer and the coexistence of a static and a dynamic transition in the behavior of the quasiparticle motion.