SU(3)三角形上的时间分辨边通量：带精确贝特曼解的合作衰变图框架
Time-Resolved Edge Flux on the SU(3) Triangle: A Cooperative-Decay Graph Framework with Exact Bateman Solutions
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中文总结 AI 辅助
该研究提出带精确贝特曼解的合作衰变图框架，将合作衰变图跃迁转化为时间相关边通量，证明其守恒等价于泡利主方程，推导辐射强度公式与广义贝特曼闭式，得到弛豫谱。
中文摘要 AI 辅助
三能级系综的合作发射通常仅通过辐射强度进行诊断，无法确定每个时刻哪些通道携带光子。我们将合作衰变图的每个跃迁转化为时间相关的边通量，证明该通量的节点守恒是泡利主方程的精确重述。假设图上存在深度函数，沿每条边递减1，则总合作速率为平均图深度的下降速度，其能量加权形式给出任意能级间距下的辐射强度I(t)=-d⟨E⟩/dt。相同的排序使生成元三角化，这从状态退出率中得到弛豫谱，同时为任意有限有向无环图上的每个布居提供广义贝特曼闭式，其中所有退出率简并被吸收为多项式乘指数的递推形式。
英文摘要
Cooperative emission from three-level ensembles is conventionally diagnosed through the radiated intensity alone, which cannot say which channels carry the photons at each instant. We promote every transition of the cooperative-decay graph into a time-dependent edge flux and show that node-wise conservation of this flux is an exact restatement of the Pauli master equation. Suppose the graph carries a depth function that decreases by one along every edge. Then the total cooperative rate is the descent speed of the mean graph depth, and its energy-weighted form gives the radiated intensity as $I(t)=-\dd\langle E\rangle/\dd t$ for arbitrary level spacings. The same ordering triangularizes the generator. This delivers the relaxation spectrum from the state exit rates, together with a generalized Bateman closed form for every population on an arbitrary finite directed acyclic graph, in which all exit-rate degeneracies are absorbed into a polynomial-times-exponential recursion.
