Localization and absorption of waves in a weakly dissipative disordered medium

The effect of a small imaginary part ε₂ to the dielectric constant on the propagation of waves in a disordered medium near the Anderson localization transition is considered. The n{→}0 replica-field representation of the averaged Green's function leads to a nonlinear {σ} model with a symmetry-breaking perturbation proportional to ε₂. In d=2+{ε}, the renormalized energy absorption coefficient is shown to increase anomalously with frequency {ω} near the mobility edge ω* as {α}{~}(ω*-{ω})^-(d-2)ν/2, {ν}=1/{ε}. It is shown that the wavelength λ* below which localization occurs is related to the elastic mean free path l by (l/λ*{)}^{d{{-}}1}${~}1/{ε} (d>2). This may occur near the limit of attainable disorder from a quenched random array of small dielectric or metallic spheres.