辐射反应与中心流形
Radiation Reaction and Center Manifolds
摘要：
研究了耦合到波场中的机械粒子在慢变势$V(\eps q)$作用下的有效动力学问题，其中$\eps$很小。在$\eps$的最低阶，粒子的运动由一个有效哈密顿量控制。在下一个顺序中，我们得到描述辐射反应的“耗散”项。我们建立，这个耗散动力学有一个中心流形，这是排斥在正常方向上，这是全球性的，在这个意义上说，对于给定的数据和足够小的$\eps$的解决方案永远停留在中心流形。我们证明了全系统的解可以很好地近似于其中心流形上的有效耗散动力学。
英文摘要：
We study the effective dynamics of a mechanical particle coupled to a wave field and subject to the slowly varying potential $V(\eps q)$ with $\eps$ small. To lowest order in $\eps$ the motion of the particle is governed by an effective Hamiltonian. In the next order one obtains ``dissipative'' terms which describe the radiation reaction. We establish that this dissipative dynamics has a center manifold which is repulsive in the normal direction and which is global, in the sense that for given data and sufficiently small $\eps$ the solution stays on the center manifold forever. We prove that the solution of the full system is well approximated by the effective dissipative dynamics on its center manifold.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
