Unified Theoretical Approach to Electronic Transport from Diffusive to Ballistic Regimes

We show that by integrating out the electric field and incorporating proper boundary conditions, a semiclassical Boltzmann equation can describe electron transport properties, continuously from the diffusive to ballistic regimes. General analytical formulas of the conductance in $D=1,2,3$ dimensions are obtained, which recover the Boltzmann-Drude formula and Landauer-B\"uttiker formula in the diffusive and ballistic limits, respectively. This intuitive and efficient approach can be applied to investigate the interplay of system size and impurity scattering in various charge and spin transport phenomena.