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 December 5, 2024)
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
Secure .gov websites use HTTPS
A lock (
) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.
Wave Localization in Binary Isotopically Disordered One-Dimensional Harmonic Chains With Impurities Having Arbitrary Cross Section and Concentration
Published
Author(s)
, 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
Issues
If you have any questions about this publication or are having problems accessing it, please contact reflib@nist.gov.
Created September 24, 2004, Updated February 19, 2017