发表机构
Zhejiang Key Laboratory of Intelligent Electromagnetic Control and Advanced Electronic Integration, College of Information Science and Electronic Engineering, Zhejiang University（浙江大学信息与电子工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出共振腔中循环散射实现非多项式计算，通过Kolmogorov-Arnold映射和微波实验验证，为线性波系统提供可控非线性计算新途径。
AI 中文摘要
结构非线性使得非线性输入-输出映射能够从原本线性的波动动力学中涌现。与输入编码结构的重复相互作用可以增强此类映射，但有限深度的实现限制了可访问的函数阶数。在此，我们展示了共振腔中的循环散射为结构非线性提供了一种独特的机制。重复相互作用被相干地累积为对结构扰动的非多项式响应。由此产生的映射自然呈现Kolmogorov-Arnold形式：扰动引起的共振频移实现内部单变量映射，而共振光谱响应提供外部映射。我们确定了表示能力的两个互补物理控制手段：共振线宽决定每个分支内的函数丰富度，而组合多个分支则扩展了可访问的函数空间。微波腔测量验证了两阶段映射，并通过XOR分类演示了双分支非线性计算。我们的结果将循环共振散射与线性波系统中可控的非多项式计算联系起来。
英文摘要
Structural nonlinearity enables nonlinear input--output mappings to emerge from otherwise linear wave dynamics. Repeated interactions with an input-encoded structure can enhance such mappings, but finite-depth implementations restrict the accessible functional order. Here we show that recurrent scattering in a resonant cavity provides a distinct regime for structural nonlinearity. Repeated interactions are coherently accumulated into a non-polynomial response to structural perturbations. The resulting mapping naturally takes a Kolmogorov--Arnold form: perturbation-induced resonance shifts realize the inner univariate mappings, while the resonant spectral response provides the outer mapping. We identify two complementary physical controls of representation capacity: the resonance linewidth governs the functional richness within each branch, whereas combining multiple branches expands the accessible function space. Microwave-cavity measurements validate the two-stage mapping and demonstrate a two-branch nonlinear computation through XOR classification. Our results connect recurrent resonant scattering with controllable non-polynomial computation in linear wave systems.
Comments6 pages, 4 figures. Supplemental Material included
