变分电动力学的化学原理与PDE
Chemical Principle and PDE of Variational Electrodynamics
摘要：
变分电动力学的两体问题具有中立型状态依赖时滞的微分时滞运动方程和在可数集上具有速度不连续性的解。从一个在断点处具有一些温和性质的周期轨道出发，在R × R ~ 3中定义了一个同步函数，并进一步利用它构造了两个在断点处消失的有界振荡函数，它们的一阶导数是连续的，且除了断点之外处处有定义.振荡函数与H2（R3）中的PDE恒等式相关联，并且我们假设PDE恒等式的排序条件以定义具有O（1/r2）自旋轨道强迫项的Fredholm-Schroedinger算子属于L2（R3）。作为应用，我们引入了化学原理判据来选择远场渐近为零的轨道，并利用根据化学原理判据选择的轨道的边界层来估计Fredholm-Schroedinger偏微分方程的玻尔半径参数。最后，向后工作，我们得到了一个化学原理一样的条件，从有序条件。
英文摘要：
The two-body problem of variational electrodynamics possesses differential-delay equations of motion with state-dependent delays of neutral type and solutions that can have velocity discontinuities on countable sets. From a periodic orbit possessing some mild properties at breaking points, we define a synchronization function in R x R3, which is further used to construct two bounded oscillatory functions vanishing at breaking points and whose first derivatives are continuous and defined everywhere but at breaking points. The oscillatory functions are associated with a PDE identity in H2(R3), and we postulate ordering conditions for the PDE identity to define a Fredholm-Schroedinger operator with an O(1/r2) spin-orbit forcing term belonging to L2(R3). As an application, we introduce the Chemical Principle criterion to select orbits with asymptotically vanishing far-fields and estimate the Bohr radius parameter of the Fredholm-Schroedinger PDE using the boundary-layer of orbits chosen according to the Chemical Principle criterion. Last, working backward, we derive a Chemical Principle-like condition from the ordering conditions.
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