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 elucidates the dynamics of collectively pinned phases occurring in any natural or synthetic elastic medium. The latter one is exemplified by a one-dimensional array of Josephson junctions, for which we specify our results. The obtained results provide benchmarks for the array-enabled quantum simulations addressing the dynamics in broader and as yet unexplored domains of individual pinning and quantum Bose glass.

• Received 1 December 2020
• Revised 18 April 2021
• Accepted 15 June 2021

DOI:https://doi.org/10.1103/PhysRevB.103.224211