One-dimensional motion in a biased random medium: Random potential versus random force

The one-dimensional motion of a particle in a biased random medium is studied in both cases of a random potential and of a random force. The correlations are not the same in both cases, and this is at the source of entirely different drift and diffusion behaviours. As a result, drift and diffusion are always normal in the presence of a random potential while anomalous motion and dynamical phase transitions may appear in the presence of a random force.