论文标题
高能颗粒通过排斥电势相互作用的稳定运动
Stable motions of high energy particles interacting via a repelling potential
论文作者
论文摘要
在轻度条件下，对于所有足够大的能量，在轻度条件下，N颗粒相互作用并局限于紧凑的D维区域的运动被证明是非凝聚的。具体而言，在高能限制下，所有颗粒均遵循几乎相同的路径，沿单个粒子系统的椭圆周期性轨道接近椭圆周期轨道，在其较高的椭圆周期轨道上，编舞溶液在高能量极限上是稳定的。最后，事实证明，矩形盒中n驱除颗粒的运动在高能下是非邻次的，可以使用一般的相互作用潜力选择：存在着一种KAM稳定周期性运动，颗粒只能在一个方向上快速移动，每个方向都在其自身的路径上移动，但与其他所有平行的移动粒子同步。
The motion of N particles interacting by a smooth repelling potential and confined to a compact d-dimensional region is proved to be, under mild conditions, non-ergodic for all sufficiently large energies. Specifically, choreographic solutions, for which all particles follow approximately the same path close to an elliptic periodic orbit of the single-particle system, are proved to be KAM stable in the high energy limit. Finally, it is proved that the motion of N repelling particles in a rectangular box is non-ergodic at high energies for a generic choice of interacting potential: there exists a KAM-stable periodic motion by which the particles move fast only in one direction, each on its own path, yet in synchrony with all the other parallel moving particles.
