Localization of elastic waves in heterogeneous media with off-diagonal disorder and long-range correlations

TL;DR

This paper investigates how elastic waves propagate in strongly heterogeneous media with various disorder types, revealing a transition to localization across dimensions, supported by analytical and numerical methods.

Contribution

It introduces a comprehensive analysis of wave localization in media with off-diagonal disorder and long-range correlations, extending understanding of elastic wave behavior in complex materials.

Findings

Localization transition occurs in any dimension due to disorder.

Long-range correlations influence the wave propagation and localization.

Numerical simulations confirm the analytical RG results.

Abstract

Using the Martin-Siggia-Rose method, we study propagation of acoustic waves in strongly heterogeneous media which are characterized by a broad distribution of the elastic constants. Gaussian-white distributed elastic constants, as well as those with long-range correlations with non-decaying power-law correlation functions, are considered. The study is motivated in part by a recent discovery that the elastic moduli of rock at large length scales may be characterized by long-range power-law correlation functions. Depending on the disorder, the renormalization group (RG) flows exhibit a transition to localized regime in {\it any} dimension. We have numerically checked the RG results using the transfer-matrix method and direct numerical simulations for one- and two-dimensional systems, respectively.