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

A random walk model in a one-dimensional disordered medium with an oscillat ory input current is presented as a generic model of boundary perturbation methods to investigate properties of a transport process in a disordered me dium. It is rigorously shown that an admittance which is equal to the Fouri er-Laplace transform of the first-passage time distribution is non-self-ave raging when the disorder is strong. The low-frequency behavior of the disor der-averaged admittance, <chi >-1 similar to omega(mu), where mu<1, does no t coincide with the low-frequency behavior of the admittance for any sample , chi-1 similar to omega. It implies that the Cole-Cole plot of <chi > appe ars at a different position from the Cole-Cole plots of chi of any sample. These results are confirmed by Monte Carlo simulations.