Range of applicability of the tunneling-hopping approximation in the quantum diffusion problem

A generalization is suggested for the tunneling-hopping approximation formulated earlier for the quantum diffusion problem. It is shown that at a fairly high concentration x and a fairly low temperature T the diffusion coefficient of an impurity is proportional to T9, which is indicative of strong localization; the relations obtained earlier remain valid at higher temperatures. Taking the correlation in the motion of impurities in the lowest temperature range into account results in a diffusion coefficient that is temperature independent and is proportional to x–n, where n ≈ 4–5.

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