The Shortest Path Across the Mesoscopic System

TL;DR

This paper investigates mesoscopic hopping conductance distributions using shortest path algorithms, confirming ergodicity and comparing results with theoretical predictions across different system dimensions.

Contribution

It introduces a numerical method based on shortest path search to study conductance distributions in mesoscopic systems, validating ergodicity and comparing with existing theories.

Findings

Distribution functions are consistent under different sampling methods.

DFs for 1D systems match theoretical predictions.

Square sample conductance distribution is nearly Gaussian.

Abstract

We study distribution functions (DF) of mesoscopic hopping conductance numerically by searching for the shortest path. We have 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 is chosen randomly, in agreement with the ergodicity hypothesis. The DFs obtained for one-dimensional systems were found to be quite close to the independent predictions of V.I. Mel'nikov, A.A. Abrikosov and P. Lee et al. For D=2, the DFs both for narrow system and thin film look similar (and close to the 1D case).The distribution function for the conductance of the square sample is nearly Gaussian as predicted by both Altshuler et al and Serota et al.