PAULI PRINCIPLE IN THE THEORY OF NONLINEAR ELECTRONIC TRANSPORT

In approaches to the theory of electronic transport, such as the Boltzmann equation and the Landauer-Buttiker formalism, the problem arises as to how to take into account the exclusion principle. Usually one introduces ad hoc statistical factors to restrict the electron final states to unoccupied levels. Such a procedure in general leads to incorrect results. This is shown by a study of the friction coefficient for a localized perturbation moving in a free-electron gas. The exact expression for the friction coefficient does not include a Pauli restriction. It is only in the case where the scattering potential has inversion symmetry or for one-dimensional systems that the Pauli term vanishes identically. Therefore, we present a detailed study using a scattering potential in two dimensions without inversion symmetry. Our numerical results show a discrepancy between the exact quantum-mechanical calculation and the probabilistic approach.