Mott's law for the critical conductance of Miller-Abrahams random resistor network

2017/12/21 by Faggionato, Alessandra
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.1712.07980

Abstract

In this short note we derive Mott's law for the critical conductance of the Miller-Abrahams random resistor network on a Poisson point process on ℝ^d, d≥ 2, and we give a percolative characterization of the factor preceding the temperature dependent term β^(α+1)/(α+1+d) . We also give mathematical arguments supporting its universality. This note is a preliminary version of a more extended work, where we also discuss the equality between the effective conductance of the resistor network and the critical conductance.

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