Click on run to see the trajectories, in real- and in velocity-space, for a single electron in an electric field. The field drives the velocity of the electron towards the left at a constant rate. The scattering time is set to such a large value that there is no visible effect of the scattering. In real space the displacement of the electron is quadratic in time, a consequence of the constant acceleration.
Reduce the scattering time tau to 3 ps. The electric field tries valiantly to push the electron off the screen, but is constantly frustrated by the collisions which keep returning the velocity of the electron to near zero. In real space, however, the electron does continue to make gradual progress to the left.