例外点动力学的Krylov层析成像与有限不确定度认证
Krylov Tomography and Finite-Uncertainty Certification of Exceptional-Point Dynamics
AI总结：
该研究针对例外点动力学的不确定度与访问范围问题，提出Krylov层析成像框架，通过有限精度模拟验证其可连接例外点结构与测量，为非厄米系统提供通用方案。
AI中文摘要：
例外点（Exceptional Points, EPs）可产生显著响应，但定位一个EP并不能揭示激发能访问其动力学的程度、探测器可区分哪些响应，也无法判断缺失信号是不存在还是未被检测到。我们提出Krylov层析成像，这是一种考虑制备与测量的框架，利用时间分辨数据和具有明确不确定度限的模型来回答上述问题，同时对偏移导致的与精确EP行为的偏离进行了界定。作为该通用框架的明确示例，我们对红边带光力模型进行了有限精度模拟，其二阶矩相干扇区包含一个三阶EP，认证了对两个和三个方向的制备敏感访问。因此，Krylov层析成像在EP结构与有限精度测量之间搭建了桥梁，为非厄米系统提供了通用框架。
英文摘要：
Exceptional points (EPs) can produce striking responses, but locating one does not reveal how much of its dynamics an excitation accesses, which responses a detector distinguishes, or whether a missing signal is absent or undetected. We introduce Krylov tomography, a preparation- and measurement-aware framework that uses time-resolved data and models with stated uncertainty limits to answer these questions, while also bounding offset-induced departures from exact-EP behavior. As an explicit illustration of the general framework, we present finite-precision simulations of a red-sideband optomechanical model, whose second-moment coherence sector contains a third-order EP, certifying preparation-sensitive access to two and three directions. Krylov tomography thus bridges EP structure and finite-precision measurements, providing a general framework for non-Hermitian systems.
