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We investigate quantum transport through strongly disordered barriers, madeof a material with exceptionally high resistivity that behaves as an Andersoninsulator or a ``bad metal'' in the bulk, by analyzing the distribution ofLandauer transmission eigenvalues for a junction where such barrier is attachedto two clean metallic leads. We find that scaling of the transmissioneigenvalue distribution with the junction thickness (starting from the singleinterface limit) always predicts a non-zero probability to find hightransmission channels even in relatively thick barriers. Using thisdistribution, we compute the zero frequency shot noise power (as well as itssample-to-sample fluctuations) and demonstrate how it provides a single numbercharacterization of non-trivial transmission properties of different types ofdisordered barriers. The appearance of open conducting channels, whosetransmission eigenvalue is close to one, and corresponding violent mesoscopicfluctuations of transport quantities explain at least some of the peculiarzero-bias anomalies in the Anderson-insulator/superconductor junctions observedin recent experiments [Phys. Rev. B {\bf 61}, 13037 (2000)]. Our findings arealso relevant for the understanding of the role of defects that can underminequality of thin tunnel barriers made of conventional band-insulators.Comment: 9 pages, 8 color EPS figures; one additional figure on mesoscopic  fluctuations of Fano facto

Quantum transparency of Anderson insulator junctions: Statistics of transmission eigenvalues, shot noise, and proximity conductance