AI 中文总结
研究团队构建了基于匹配左、右本征算子的刘维尔算子可操作谱理论，将其应用于受驱克尔谐振器，实现了模式选择性抑制、弛豫通道分离等功能，补充了刘维尔算子本征值的信息。
AI 中文摘要
刘维尔算子的本征值决定了衰减率和振荡频率，但无法决定对应模式在选定协议中的激发、传播与检测方式。我们基于匹配的左、右本征算子构建了一套可操作谱理论：左本征算子决定输入或源的激发过程，右本征算子决定传播的密度形变与读出重叠，二者的乘积为规范不变的模态权重。对于玻色系统，相干制备将左本征算子转化为相空间激发映射，其零点对应模式选择性抑制；右本征算子则给出对应的维格纳形变。分辨慢子空间定义了可操作坐标，且在正性与马尔可夫可容性成立时，可得到投影路由生成元。在受驱克尔谐振器中，该框架可识别抑制开关模式的制备方案，分离对称性分辨的弛豫通道，并揭示投影多通道路由中由偏置诱导的交叉现象，而相干制备划分仍持续发生形变。因此，制备几何与慢扇区传播提供了仅靠刘维尔算子本征值无法提供的互补可操作信息。
英文摘要
Liouvillian eigenvalues determine decay rates and oscillation frequencies, but not how the corresponding modes are excited, propagated, and detected in a chosen protocol. We develop an operational spectral theory based on matched left and right eigenoperators. Left eigenoperators determine excitation by an input or source; right eigenoperators determine the propagated density deformation and readout overlap; their product is a gauge-invariant modal weight. For bosonic systems, coherent preparations turn left eigenoperators into phase-space excitation maps whose zeros identify mode-selective suppression, while right eigenoperators yield the corresponding Wigner deformations. Resolved slow subspaces define operational coordinates and, when positivity and Markov-admissibility hold, a projected routing generator. In driven Kerr resonators, the framework identifies preparations that suppress a switching mode, separates symmetry-resolved relaxation channels, and reveals bias-induced crossovers in projected multichannel routing while the coherent-preparation partition continues to deform. Preparation geometry and slow-sector propagation thus provide complementary operational information beyond Liouvillian eigenvalues alone.
Comments19 pages, 7 figures, comments are welcome
