Precise asymptotics for a variable-range hopping model

TL;DR

This paper provides precise asymptotic analysis of a modified variable-range hopping model to better understand finite-temperature conductivity in localized electron systems, building on Mott's theory.

Contribution

It introduces exact asymptotic results for a modified hopping model, advancing the mathematical understanding of electron conduction at finite temperatures.

Findings

Derived precise asymptotics for the modified model

Enhanced understanding of variable-range hopping behavior

Bridged theoretical predictions with mathematical rigor

Abstract

For a system of localised electron states the DC conductivity vanishes at zero temperature, but localised electrons can conduct at finite temperature. Mott gave a theory for the low-temperature conductivity in terms of a variable-range hopping model, which is hard to analyse. Here we give precise asymptotic results for a modified variable-range hopping model proposed by S. Alexander [Phys. Rev. B 26, 2956 (1982)].