Spatiotemporal Structures of Parametrically Driven Nonlinear Lattices

Yu Funami; Kazushi Aoyama

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arXiv · 2605.26668

Spatiotemporal Structures of Parametrically Driven Nonlinear Lattices

Yu Funami·Kazushi Aoyama

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Abstract

We theoretically investigate the effects of parametric driving on the one-dimensional Frenkel-Kontorova model, a nonlinear many-body lattice system. It is numerically found that a parametric vibration induces spatiotemporal ordering characterized by the subharmonic frequency $\omega_{\mathrm{ex}}/2$ and wavenumber $k$ which takes nontrivial values depending on the vibration strength $P_{\mathrm{ac}}$ and frequency $\omega_{\mathrm{ex}}$. With increasing $P_{\mathrm{ac}}$, $k$ gradually increases and discontinuously jumps up to $k=\pi$. Based on an extended linear stability analysis, we show that the former $k$ resonance (the latter $\pi$ resonance) corresponds to the unstable (stable) mode and that the $k$ resonance is made possible by the interplay between the parametric amplification and the collective fluctuation developing through the nonlinear effect.

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Yu Funami, Kazushi Aoyama. 2026-05-26. Spatiotemporal Structures of Parametrically Driven Nonlinear Lattices. https://arxiv.org/abs/2605.26668

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