Drift-controlled anomalous diffusion: A solvable Gaussian model

We introduce a Langevin equation characterized by a time-dependent drift. B y assuming a temporal power-law dependence of the drift, we show that a gre at variety of behavior is observed in the dynamics of the variance of the p rocess. In particular, diffusive, subdiffusive, superdiffusive, and stretch ed exponentially diffusive processes are described by this model for specif ic values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxatio n to the stationary solution has a power-law behavior in time with an expon ent controlled by one of the model parameters.