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Anderson Localization Phenomenon in One-Dimensional Elastic Systems

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Méndez-Sánchez R., Gutiérrez L., Morales A., Flores J., Díaz-de-Anda A., Monsivais G.
Acta Physica Polonica A
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2013
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vol. 124
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issue 6
1063-1068
EN
The phenomenon of the Anderson localization of waves in elastic systems is studied. We analyze this phenomenon in two different sets of systems: disordered linear chains of harmonic oscillators and disordered rods which oscillate with torsional waves. The first set is analyzed numerically whereas the second one is studied both experimentally and theoretically. In particular, we discuss the localization properties of the waves as a function of the frequency. In doing that we have used the inverse participation ratio, which is related to the localization length. We find that the normal modes localize exponentially according to the Anderson theory. In the elastic systems, the localization length decreases with frequency. This behavior is in contrast with what happens in analogous quantum mechanical systems, for which the localization length grows with energy. This difference is explained by means of the properties of the reflection coefficient of a single scatterer in each case.
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