AI 中文总结
SAKE是用于量子动力学模型间非线性光谱响应传输的可微计算框架，结合自动微分与杜哈梅尔理论，经四能级激子二聚体验证，可高效支持参数探索、灵敏度分析及逆设计应用。
AI 中文摘要
我们引入谱自动微分核展开（Spectral Autodiff Kernel Expansion, SAKE），这是一种可微计算框架，用于在相邻量子动力学模型间传输非线性光谱响应。与针对每个哈密顿量或刘维尔量独立重新计算多维光谱不同，SAKE通过将前向模式自动微分与杜哈梅尔传输理论相结合，构建关于参考模型的局部传输展开。自动微分生成参数依赖刘维尔量的一阶、二阶和三阶导数，这些导数被组装成路径传输算子，将参考模型的非线性响应映射到相邻系统。该框架针对具有su(2)×su(2)对称性的四能级激子二聚体进行验证，将二阶和三阶传输路径算子与直接计算得到的精确投影传输矩阵进行比较。三阶展开能准确再现投影传输算子及其相关的路径混合。除提供高效计算策略外，该传输算子还揭示了相干与耗散扰动如何在双面费曼路径间重新分配振幅，展现出非线性光谱无法直接呈现的机制信息。SAKE因此建立了一种用于非线性光谱的可微计算框架，支持高效的局部参数探索、灵敏度分析及未来的逆设计应用。
英文摘要
We introduce the Spectral Autodiff Kernel Expansion (SAKE), a differentiable computational framework for transporting nonlinear spectroscopic response between neighboring quantum dynamical models. Rather than recomputing multidimensional spectra independently for each Hamiltonian or Liouvillian, SAKE constructs local transport expansions about a reference model by combining forward-mode automatic differentiation with Duhamel transport theory. Automatic differentiation generates first-, second-, and third-order derivatives of the parameter-dependent Liouvillian, which are assembled into a pathway transport operator that maps the nonlinear response of a reference model onto neighboring systems. The framework is validated for a four-level excitonic dimer possessing an $su(2)\times su(2)$ symmetry by comparing second- and third-order transported pathway operators with exact projected transport matrices obtained from direct calculations. The third-order expansion accurately reproduces the projected transport operator and its associated pathway mixing. Beyond providing an efficient computational strategy, the transport operator reveals how coherent and dissipative perturbations redistribute amplitude among double-sided Feynman pathways, exposing mechanistic information that is not directly apparent from the nonlinear spectrum. SAKE thereby establishes a differentiable computational framework for nonlinear spectroscopy that supports efficient local parameter exploration, sensitivity analysis, and future inverse-design applications.
