2023/01/16 by Alessandra Faggionato, Faggionato, Alessandra · 1 citation
Materials Science · Physics and Astronomy · #60G55 #82B43 #82D30 #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Force Microscopy Techniques and Applications #Mathematical Physics (math-ph) #Probability (math.PR) #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics #Thermal properties of materials
paper · pdf · doi:10.48550/arxiv.2301.06318
openalex publication_date 2023/01/16 · openalex created_date 2023/01/19 · openalex updated_date 2026/07/28
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, 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 \cite[Section~IV]AHL 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.