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 ${\mathit{t}}^{9/8}$ for d>1, and as ${\mathit{t}}^{6/5}$ in d=1. Its kinetic energy increases as ${\mathit{t}}^{1/2}$ for d>1, and as ${\mathit{t}}^{2/5}$ 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.