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PreprintCC BY 4.0arXiv

Anderson localization in periodic elastic systems with random perturbations

  • Xin Feng
  • Peijun Li
  • Wei Wu
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Abstract

This paper investigates Anderson localization in subwavelength elastic periodic systems with random perturbations. For the unperturbed system, we use layer potential techniques to reformulate the eigenvalue problem as boundary integral equations, and derive asymptotic formulas for the subwavelength eigenvalues. For perturbed systems, we apply the Floquet transform to obtain a periodic formulation and derive equations determining the resonant frequencies under general perturbations. Numerical experiments for perturbed periodic monomers and dimers agree with the theoretical predictions. We further demonstrate Anderson localization by increasing the strength and number of random perturbations. These results provide a mathematical foundation for understanding subwavelength localization in elastic metamaterials.

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Cite

BibTeXRIS
BibTeX
@misc{feng2026anderson,
  title = {{Anderson localization in periodic elastic systems with random perturbations}},
  author = {Xin Feng and Peijun Li and Wei Wu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2609.14410},
  eprint = {2609.14410},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.14410},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Anderson localization in periodic elastic systems with random perturbations
AU  - Xin Feng
AU  - Peijun Li
AU  - Wei Wu
PY  - 2026
DA  - 2026/10/06
PB  - arXiv
DO  - 10.48550/arxiv.2609.14410
UR  - https://arxiv.org/abs/2609.14410
AB  - This paper investigates Anderson localization in subwavelength elastic periodic systems with random perturbations. For the unperturbed system, we use layer potential techniques to reformulate the eigenvalue problem as boundary integral equations, and derive asymptotic formulas for the subwavelength eigenvalues. For perturbed systems, we apply the Floquet transform to obtain a periodic formulation and derive equations determining the resonant frequencies under general perturbations. Numerical experiments for perturbed periodic monomers and dimers agree with the theoretical predictions. We further demonstrate Anderson localization by increasing the strength and number of random perturbations. These results provide a mathematical foundation for understanding subwavelength localization in elastic metamaterials.
ER  -