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

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

2000-12-25

arxiv.org/abs/cond-mat/0012457v1

Phys. Rev. B 61 (2000) 5839

Physics

Condensed Matter

Disordered Systems and Neural Networks

7 pages, 2 figures, published in Phys. Rev. B

Scientific paper

10.1103/PhysRevB.61.5839

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, $<\chi > -1 \sim \omega^{\mu}$ where $\mu < 1$, does not coincide with the low frequency behavior of the admittance for any sample, $\chi - 1 \sim \omega$. It implies that the Cole-Cole plot of $<\chi>$ appears at a different position from the Cole-Cole plots of $\chi$ of any sample. These results are confirmed by Monte-Carlo simulations.

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