Position broadening effect in hot-electron transport

We utilize the Kadanoff-Baym-Keldysh methods to develop a formalism appropriate for high, homogeneous fields. The aim is to derive a spectral density model which can account for both the energy dependence of the collision rate and the intracollisional field effect in a relatively simple and rigorous way. We solve the appropriate Dyson's equation in the first Born approximation for the case of scattering mechanisms described by a momentum-independent self-energy. We obtain an analytical expression for the spectral density and derive an integral equation for the correlation function G^<, which is proportional to the density of particles. We show that the field, acting in conjunction with the phonons, leads to an effective quantization of the energy in the direction of the electric field suggesting the presence of a novel quantum effect consisting in a discontinuous trajectory of the electron along this direction.