Wave Localization in Binary Isotopically Disordered One-Dimensional Harmonic Chains With Impurities Having Arbitrary Cross Section and Concentration

Published

September 24, 2004

Author(s)

Kenneth A. Snyder, T R. Kirkpatrick

Abstract

The localization length is calculated for harmonic one-dimensional lattices havingbinary (isotopic) disorder. The results are applicable to classical strongly scattered systems having arbitrary wavelength, impurity cross section, and impurity concentration. The scattering cross section is corrected for the wavelength dependent pulse propagation speed, and the scattering cross section is shown to be symmetric about zero, with respect to the mass added to, or subtracted from, the original background mass. Moreover, it is shown that pairs of systems having changes in mass symmetric about zero, and thus having the same impurity cross section, have different localization behavior at high concentration. For all binary systems, there is a minimum localization length that is a function of the displacement wavelength, impurity cross section, and impurity concentration. The behavior over the entire impurity concentration range isapproximated accurately by a sum of two independent systems, each characterizing the limiting behavior at each concentration limit.Measurements of Lyapunov exponent statistics indicate practical limits for the minimum system length and number of scatterers to achieve representative ensemble averages. These results are applicable to polymeric systems and spectroscopy, and are necessary for understanding numerical experiments on discrete anharmonic systems that must exploit short wavelengths and strong scattering to be practical.

Citation

Physical Review B (Condensed Matter and Materials Physics)

Pub Type

Journals

Keywords

energy transport, isotopic disorder, localization, Lyapunov exponent, one-dimensional chains

Citation

Snyder, K. and Kirkpatrick, T. (2004), Wave Localization in Binary Isotopically Disordered One-Dimensional Harmonic Chains With Impurities Having Arbitrary Cross Section and Concentration, Physical Review B (Condensed Matter and Materials Physics) (Accessed April 23, 2024)