Self-trapping and time evolution in some spatially extended quantum nonlinear systems: Exact solutions

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Abstract
We present exact analytical solutions of the discrete nonlinear Schro¨dinger equation for N-site systems by generalizing methods employed previously for the quantum nonlinear dimer and trimer. The transition from localized to delocalized states is markedly different from that in the dimer. A transition, for which there is no dimer analog, occurs in which an initial excitation that is partially localized over a group of sites is found to be partially localized over these same sites or over a different group of sites depending on the strength of the nonlinearity and the asymmetry of the lattice.