Drift-controlled anomalous diffusion: A solvable Gaussian model

We introduce a Langevin equation characterized by a time-dependent drift. By assuming a temporal power-law dependence of the drift, we show that a great variety of behavior is observed in the dynamics of the variance of the process. In particular, diffusive, subdiffusive, superdiffusive, and stretched exponentially diffusive processes are described by this model for specific values of the two control parameters. The model is also investigated in the presence of an external harmonic potential. We prove that the relaxation to the stationary solution has a power-law behavior in time with an exponent controlled by one of the model parameters.