Quantized conductance without the reservoir picture

We derive a set of quantum kinetic equations based on quantum mechanical balance equations. The quantum kinetic equations are solved self-consistently together with Poisson's equation. We show that these kinetic equations can be used to rederive the Landauer formula for the conductance of a quantum point contact, without any reference to reservoirs at different chemical potentials. Instead, energy dissipation is taken into account explicitly through the electron-phonon interaction. We find that both elastic and inelastic scattering are necessary to obtain the Landauer conductance.