Distribution Function of Mesoscopic Hopping Conductance

We study mesoscopic hopping conductance by computer simulation distribution functions(DFs),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 randmly,in agreement with the ergodicity hypothesis.The DFs in shape obtained for one-dimensional system 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 DF for the conductance of the square sample is nearly Gaussian.