Effective noise theory for the NLSE

For the Nonlinear Shrödinger Equation with disorder it was found numerically that in some regime of the parameters Anderson localization is destroyed and subdiffusion takes place for a long time interval. It was argued that the nonlinear term acts as random noise. In the present work the properties of this effective noise were studied numerically. Some assumptions made in earlier work were verified, and fine details were obtained. The dependence of various quantities on the localization length of the linear problem were computed. A scenario for the possible breakdown of the theory for a very long time will be outlined.