Low density of random elastic scatterers provides a long-range correlation between transmitted and incident wave functions in any dimensionality. Exact formulas prove it. They also demonstrate different localization lengths for different quantities. The experimental implications are strong localization in very pure wires at reasonable temperatures and periodical resonance-type minima and maxima of a residual resistance in a static magnetic field. The results are also true for any (e.g., electromagnetic wave) random scattering.
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M. Ya. Azbel (1981) studied this question.
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