Classical and quantum superdiffusion in a time-dependent random potential

We consider wandering of a nonrelativistic particle in a time-dependent random potential in d spatial dimensions. Its root-mean-square displacement from the initial position increases superdiffusively with time t as t9/8 for d>1, and as t6/5 in d=1. Its kinetic energy increases as t1/2 for d>1, and as t2/5 in d=1. These scaling behaviors hold for both the classical and the corresponding quantum-mechanical problem in continuous space-time and differ from those of lattice models.