Mott's law for the v.r.h. random resistor network and for Mott's random walk

• 成果类型: Article
• 署名作者: Faggionato, Alessandra
• 署名单位: Sapienza University Rome
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051; 1432-2064
• DOI: 10.1007/s00440-025-01463-9
• 发表日期: 2026-02
• 页码: 1-40
• 关键词: Marked simple point process; Poisson point process; Mott's random walk; Random resistor network for v.r.h.; Mott's law; percolation; Stochastic Homogenization; invariance-principle; HOPPING CONDUCTIVITY

摘要

Mott's variable range hopping (v.r.h.) is the phonon-induced hopping of electrons in disordered solids (such as doped semiconductors) within the regime of strong Anderson localization. It was introduced by N. Mott to explain the anomalous low temperature conductivity decay in dimension d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 2$$\end{document}, corresponding now to the so called Mott's law. We provide a rigorous derivation of this Physics law for two effective models of Mott v.r.h.: the random resistor network for v.r.h. of [1, Section IV] and Mott's random walk. We also determine the constant multiplying the power of the inverse temperature in the exponent in Mott's law, which was an open problem also on a heuristic level.