Non linear transport in drift-diffusion equations under magnetic field

We analyze numerically and analytically the non linear transport properties of a drift-diffusion equation in presence of a magnetic field and of a disorder potential. For a wide range of parameters this model exhibits a plateau where the drift velocity is almost independent on the applied electric field. This behavior has strong similarities with the zero differential resistance states observed experimentally in high mobility two dimensional systems. Performed numerical simulations are in a good global agreement with the developed analytical theory even if the later leads to overestimated negative differential resistance values.