用于X射线超荧光的厄米随机方法
Hermitian stochastic methodology for X-ray superfluorescence
AI总结：
针对X射线放大自发辐射随机模型的发散与数值不稳定问题，提出微扰处理随机分量的厄米形式体系，可统一描述各发射阶段并使单次随机实现对应单次实验观测。
摘要：
最近引入的一种用于模拟X射线放大自发辐射动力学的理论框架，基于对量子发射体密度矩阵和辐射场的随机采样，类似于其他相空间采样技术。尽管该框架基于第一性原理并能提供有价值的理论洞见，但原始随机微分方程存在发散和数值不稳定性。在这里，我们通过以微扰方式处理随机分量来解决这一问题。改进后的形式体系能够准确再现自发辐射的性质，并被证明普遍适用于描述近轴几何中集体X射线发射的所有阶段，包括自发辐射、放大自发辐射以及非线性区域。通过数值算例，我们分析了一维近似下超荧光的关键特征。重要的是，底层随机方程的单次实现可以被完全解释为对超荧光的单次实验观测。
英文摘要：
A recently introduced theoretical framework for modeling the dynamics of X-ray amplified spontaneous emission is based on stochastic sampling of the density matrix of quantum emitters and the radiation field, similarly to other phase-space sampling techniques. While based on first principles and providing valuable theoretical insights, the original stochastic differential equations exhibit divergences and numerical instabilities. Here, we resolve this issue by accounting the stochastic components perturbatively. The refined formalism accurately reproduces the properties of spontaneous emission and proves universally applicable for describing all stages of collective X-ray emission in paraxial geometry, including spontaneous emission, amplified spontaneous emission, and the non-linear regime. Through numerical examples, we analyze key features of superfluorescence in one-dimensional approximation. Importantly, single realizations of the underlying stochastic equations can be fully interpreted as individual experimental observations of superfluorescence.
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