Localization-delocalization transition and subdiffusion of discrete nonlinear Schrödinger equation in three dimensions.

Localization-delocalization transition in a three-dimensional discrete nonlinear Schrödinger equation (DNLSE) with random potential is investigated, and the effect of nonlinearity is clarified numerically. By Thouless-number analysis, it is shown that the nonlinearity tends to delocalize the stationary states in a three-dimensional DNLSE. The spreading of a wave packet in a localized regime is also clarified for this system, and the subdiffusive behavior is observed in the three-dimensional system when the nonlinearity of the system is sufficiently strong. In addition, a one-dimensional DNLSE with random potential having a finite correlation length is studied, and it is suggested that the power-law exponent of the subdiffusion in DNLSE is not a universal quantity.