Distribution Function of Mesoscopic Hopping Conductance

We study mesoscopic hopping conductance by computer simulation
distribution functions (DF). It is found that the distributions obtained by choosing randomly the chemical potentials (for a fixed impurity configuration), which corresponds to a typical experimental situation, coincide with those obtained when both impurity configuration and chemical potential are chosen randomly, in agreement with the ergodicity hypothesis. The DFs in shape obtained for one-dimensional systems are found to be quite close to the predictions of the theory by Raikh and Ruzin. For the two-dimensional case, the DFs both for a narrow system and thin film look to be similar (and close to the one-dimensional case). The distribution function for the conductance of the square sample is nearly Gaussian.