Generalized dynamic-disorder transport rule with application to the study of temporal correlation effects

Abstract

A new relation giving average transport behavior for dynamically disordered systems in terms of that for static disorder follows by considering the statistical growth of mean-square carrier displacement. The result is more widely applicable than the D(ω)→D(ω-iλ) analytic continuation rule (for average reinitialization rate λ) originally derived for bond percolation on a periodic lattice, and reproduces earlier results in appropriate limits, thereby showing the analytic continuation rule and other earlier results to apply more generally than previously demonstrated, applying for example to a continuous distribution of hopping rates, to nonperiodic arrays of sites, and to site percolation as well as bond percolation. Application to a study of temporal correlation between reinitialization events in a bond-percolation model shows these effects to be small but non-negligible, demonstrating the applicability of the previous analytic continuation rule as a reasonable approximation under conditions where temporal correlation makes it inexact.