Transport of localized and extended excitations in a nonlinear Anderson model

We study the propagation of electrons (or excitations) through a one-dimens ional tight-binding chain in the simultaneous presence of nonlinearity and diagonal disorder. The evolution of the system is given by a disordered ver sion of the discrete nonlinear Schrodinger equation. For an initially local ized excitation we examine its mean square displacement [n(2)(t)] for relat ively long times Vt similar to 10(4), for different degrees of nonlinearity . We found that the presence of nonlinearity produces a subdiffusive propag ation [n(2)(t)]similar to t(alpha), with alpha similar to 0.27 and dependin g weakly on nonlinearity strength. This nonlinearity effect seems to persis t for a long time before the system converges to the usual Anderson model. We also compute the transmission of plane waves through the system. We foun d an average transmissivity that decays exponentially with system size [T]s imilar to exp(-beta L), where beta increases with nonlinearity. We conclude that the presence of nonlinearity favors (inhibits) the propagation of loc alized (extended) excitations. [S0163-1829(98)06340-1].