Wave propagation and localization in a long-range correlated random potential
- 1 December 1983
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 28 (11), 6358-6368
- https://doi.org/10.1103/physrevb.28.6358
Abstract
We examine the effect of long-range spatially correlated disorder on the Anderson localization transition in dimensions. This is described as a phase transition in an appropriate non-linear model. We consider a model of scalar waves in a medium with an inhomogeneous index of refraction characterized by scattering strength and spatial correlations of range decaying (i) exponentially and (ii) by power laws . A replica-field-theory representation is utilized in the calculation of the one- and two-particle Green's functions. In addition to the usual diffusive Goldstone mode of the field theory arising from energy conservation, the non-linear model is shown to possess a discrete spectrum of low-lying nondiffusive modes associated with approximate wave-vector () conservation in the geometric optics limit . For waves it is shown that all states are localized for with diverging localization lengths in the low-frequency limit and that the mobility edge in separating high-frequency, localized states from low-frequency, extended states is characterized by the same critical exponents as for spatially uncorrelated disorder provided . The problem of electron localization in a long-range correlated random potential is also described within the same universality class.
Keywords
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