Building and Destroying Symmetry in 1-D Elastic Systems
J. Flores, G. Monsivais, P. Mora, A. Morales, R. A., M\'endez-S\'anchez, A. D\'iaz-de-Anda, and L. Guti\'errez
TL;DR
This paper explores how introducing defects into 1-D elastic systems affects their spectral properties, demonstrating phenomena like band spectra, Wannier-Stark ladders, and Anderson localization with experimental validation.
Contribution
It presents a systematic study of symmetry breaking in 1-D elastic systems and experimentally confirms the theoretical predictions for various defect configurations.
Findings
Periodic rods exhibit band spectra.
Defects can induce Wannier-Stark ladders.
Random defects lead to Anderson localization.
Abstract
Locally periodic rods, which show approximate invariance with respect to translations, are constructed by joining unit cells. The spectrum then shows a band spectrum. We then break the local periodicity by including one or more defects in the system. When the defects follow a certain definite prescription, an analog of the Wannier-Stark ladders is gotten; when the defects are random, an elastic rod showing Anderson localization is obtained. In all cases experimental values match the theoretical predictions.
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