Boltzmann treatment of nanoscale inhomogeneous electrical conduction

Small distance scales (e.g. boundaries of small samples) destroy the propagating electron quasiparticles that Boltzmann transport theory needs. Our model retains propagating single particle electrons, but generates nanoscale inhomogeneities by introducing nanoscale source terms In the Boltzmann equation of a macroscopic homogeneous metal. We solve the equations in Fourier space for electron distribution functions arising from charge input ~exp(iqx). Fourier transformation allows computation of fields the E(x), V(x), and n(x) corresponding to currents j(x) derived from a realistic charge input from discrete electrodes. We study the ballistic to diffusive crossover as the sample size and electrode size are varied on distance scales comparable to the electron mean free path.