用于耗散系统的马格努斯生成器及其在领先的 2.5PN 辐射反应动力学中的应用
The Magnusian generator for dissipative systems and application to leading 2.5PN radiation-reaction dynamics
- Max Planck Institute for Gravitational Physics (Albert Einstein Institute)（马克斯·普朗克引力物理研究所（爱因斯坦研究所））
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究将马格努斯框架扩展到含耗散和非局域时间相互作用的系统，利用含时演化形式推导广义马格努斯量。以牛顿束缚运动受 2.5PN 辐射反应力为例，构建马格努斯量，其生成的离散演化映射与数值解相符。
AI中文摘要：
马格努斯量是一种通过嵌套泊松括号生成有限时间演化的相空间函数，与经典动力学的几个常见生成器相关。本文利用含时演化形式（又称施温格 - 凯尔迪什或加利形式）将马格努斯框架扩展到具有耗散和非局域时间相互作用的系统。该框架对双星动力学很自然，积分掉中介引力场可产生耗散辐射反应效应和遗传的非局域时间相互作用。我们推导了广义马格努斯量并表明它继续生成有限时间演化。作为应用，构建了受领先的 2.5PN 辐射反应力作用的牛顿束缚运动的马格努斯量，所得生成器定义了从一个周期到下一个周期的离散演化映射，且与数值解一致地描述了系统演化。
英文摘要：
The Magnusian is a phase-space function that generates finite-time evolution through nested Poisson brackets. It is related to several familiar generators of classical dynamics, including the radial action, the eikonal phase and related quantities. In this work, we extend the Magnusian framework to systems with dissipation and nonlocal-in-time interactions using the in-in formalism, also known as the Schwinger-Keldysh or Galley formalism. This framework is particularly natural for binary dynamics, where integrating out the mediating gravitational field can produce both dissipative radiation-reaction effects and hereditary, nonlocal-in-time interactions. We derive the generalized Magnusian and show that it continues to generate finite-time evolution. As an application, we construct the Magnusian for Newtonian bound motion subject to the leading 2.5PN radiation-reaction force. The resulting generator defines a discrete evolution map from one cycle to the next and describes the evolution of the system in agreement with numerical solutions.
