Absence of self-averaging in the complex admittance for transport through random media

Abstract

A random walk model in a one dimensional disordered medium with an oscillatory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered medium. It is rigorously shown that an admittance which is equal to the Fourier-Laplace transform of the first-passage time distribution is non-self-averaging when the disorder is strong. The low frequency behavior of the disorder-averaged admittance, $<χ> -1 \sim ω^μ$ where $μ< 1$, does not coincide with the low frequency behavior of the admittance for any sample, $χ- 1 \sim ω$. It implies that the Cole-Cole plot of $<χ>$ appears at a different position from the Cole-Cole plots of $χ$ of any sample. These results are confirmed by Monte-Carlo simulations.