2025/03/30 by Pedro L. Garrido, Tomasz Komorowski, Garrido, Pedro L. +5 · 2 citations
Computer Science · #80A05 #82C22 #82C70 #Contact Mechanics and Variational Inequalities #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · pdf · doi:10.48550/arxiv.2503.23527
openalex publication_date 2025/03/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We study the propagation of energy in one-dimensional anharmonic chains subject to a periodic, localized forcing. For the purely harmonic case, forcing frequencies outside the linear spectrum produce exponentially localized responses, preventing equi-distribution of energy per degree of freedom. We extend this result to anharmonic perturbations with bounded second derivatives and boundary dissipation, proving that for small perturbations and non-resonant forcing, the dynamics converges to a periodic stationary state with energy exponentially localized uniformly in the system size. The perturbed periodic state is described by a convergent power type expansion in the strength of the anharmonicity. This excludes chaoticity induced by anharmonicity, independently of the size of the system. Our perturbative scheme can also be applied in higher dimensions.