Numerical studies of variable-range hopping in one-dimensional systems

TL;DR

This paper presents numerical analysis of variable-range hopping in 1D systems, introducing a fast algorithm for resistance pathfinding, analyzing resistance distributions, and contrasting Ohmic and non-Ohmic regimes.

Contribution

It introduces a novel fast algorithm for finding the lowest-resistance path and provides detailed statistical analysis of resistance fluctuations in 1D hopping transport.

Findings

Resistance distributions fitted to analytic formulas

Differences in resistance fluctuation statistics between regimes

Comparison with prior theoretical and experimental results

Abstract

Hopping transport in a one-dimensional system is studied numerically. A fast algorithm is devised to find the lowest-resistance path at arbitrary electric field. Probability distribution functions of individual resistances on the path and the net resistance are calculated and fitted to compact analytic formulas. Qualitative differences between statistics of resistance fluctuations in Ohmic and non-Ohmic regimes are elucidated. The results are compared with prior theoretical and experimental work on the subject.