SELF-TRAPPING AND TIME EVOLUTION IN SOME SPATIALLY EXTENDED QUANTUM NONLINEAR-SYSTEMS - EXACT-SOLUTIONS

We present exact analytical solutions of the discrete nonlinear Schrodinger 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.