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Random walk models in one-dimensional disordered media with an oscillatoryinput current are investigated theoretically as generic models of the boundaryperturbation experiment. It is shown that the complex admittance obtained inthe experiment is not self-averaging when the jump rates $w_i$ are randomvariables with the power-law distribution $\rho(w_i)\sim {w_i}^{\alpha-1} (0 <\alpha \leq 1)$. More precisely, the frequency-dependence of thedisorder-averaged admittance $<\chi>$ disagrees with that of the admittance$\chi$ of any sample. It implies that the Cole-Cole plot of $<\chi>$ shows adifferent shape from that of the Cole-Cole plots of $\chi$ of each sample. Thecondition for absence of self-averaging is investigated with a toy model interms of the extended central limit theorem. Higher dimensional media are alsoinvestigated and it is shown that the complex admittance for two-dimensional orthree-dimensional media is also non-self-averaging.Comment: 38 pages, 18 figures, submitted to Phys. Rev. B. Section VII was  revised completely with the new results for higher dimensional disordered  medi

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