Transmission of waves through a pinned elastic medium

We investigate the scattering of elastic waves off a disordered region described by a one-dimensional random-phase sine-Gordon model. The collective pinning results in an effective static disorder potential with universal and non-Gaussian correlations, acting on propagating waves. We find signatures of the correlations in the wave transmission in a wide frequency range, which covers both the weak and strong localization regimes. Our theory works for any elastic medium. One-dimensional Josephson junction arrays provide an example where our results can be applied to detect and study the insulating "Bose-glass" phase using the microwave impedance data.