Quantum continuous time random walk in nonlinear Schrödinger equation with disorder

A quantum nonlinear Schrödinger equation in the presence of disorder is considered. The dynamics of an initially localized wave packet is studied and subdiffusion of the wave packet is obtained with a transport exponent 1/2. It is shown that this transport exponent has pure quantum nature. A probabilistic description of subdiffusion in the framework of a quantum continuous time random walk is suggested and a quantum master equation is obtained.