Quantum resistance of a Cayley tree composed of one-dimensional random scatterers is considered. The strength of a scatterers is characterized by its typical resistance ρ₀. It is shown that a metal-insulator transition occurs at some critical scattering strength ρ0c, which depends on the coordination number of the tree. The resistance of an infinite tree diverges for ρ₀>ρ0c and saturates at some finite value for ρ₀<ρ0c.
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Boris Shapiro (1983) studied this question.
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