Random elastic scattering: Long-range correlation and localization

Abstract

In any dimensionality a transfer matrix is rigorously introduced for any type of an elastic scattering (quantum particle, electromagnetic waves, etc.) by arbitrarily situated scatterers with nonoverlapping projections on a certain axis. An exact formula for the transfer-matrix ensemble average is presented. The derived individual scattering model provides the exact formula for any scattering characteristic. Scattering ensemble averages for randomly situated scatterers demonstrate a strong long-range correlation between incident and transmitted waves (rather than commonly accepted complete phase randomization), a resonance transmission and resistance dependence on the incident wave vector, and different localization lengths for different quantities. Resistance resonance minima and maxima may be observed at certain values of a static magnetic field. A strong localization in very pure and perfect wires is possible. An experimental observation of any of these phenomena would demonstrate the elastic random-scattering long-range correlation. An electromagnetic wave scattering may be a model for an electron localization. The obtained transfer matrix reduces the scattering to a certain free energy.