Wave propagation and localization in a long-range correlated random potential

This is the authors' abstract. We don't add key points for this paper.

We examine the effect of long-range spatially correlated disorder on the Anderson localization transition in d=2+ε dimensions. This is described as a phase transition in an appropriate non-linear σ model. We consider a model of scalar waves in a medium with an inhomogeneous index of refraction characterized by scattering strength γ² and spatial correlations of range a decaying (i) exponentially γ₁²a^-de^-x/a and (ii) by power laws γ₂²(a²+x²)^-m(m>0). 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 σ model is shown to possess a discrete spectrum of low-lying nondiffusive modes associated with approximate wave-vector (→k) conservation in the geometric optics limit ka1. For waves it is shown that all states are localized for d≤2 with diverging localization lengths in the low-frequency limit and that the mobility edge in d=2+ε separating high-frequency, localized states from low-frequency, extended states is characterized by the same critical exponents as for spatially uncorrelated disorder provided m>ε. The problem of electron localization in a long-range correlated random potential is also described within the same universality class.