Localization properties of acoustic waves in the random-dimer media

Propagation of acoustic waves in the one-dimensional (1D) random-dimer (RD) medium is studied by three distinct methods. First, using the transfer-matrix method, we calculate numerically the localization length xi of acoustic waves in a binary chain (one in which the elastic constants take on one of two values). We show that when there exists short-range correlation in the medium-which corresponds to the RD model-the localization-delocalization transition occurs at a resonance frequency omega(c). The divergence of xi near omega(c) is studied, and the critical exponents that characterize the power-law behavior of xi near omega(c) are estimated for the regimes omega>omega(c) and omega