实现类库仑相互作用的纯力学系统
A purely mechanical system realizing a Coulomb-like interaction
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中文总结 AI 辅助
本文以闭式解求解一维相对论弹性碰撞系统，揭示无质量中介体产生离散库仑势，有质量中介体产生1/r^3力，并构造了库仑原子的力学类比。
中文摘要 AI 辅助
我们以闭式解求解了一个一维相对论系统：两个质量体仅通过与在其间弹跳的无质量中介体的弹性碰撞相互作用。动量、时间和位置是碰撞指数的双曲函数。中介体能量被解释为该对的等效势能，满足精确的离散库仑定律，$V\propto 1/r$，并以洛伦兹不变的作用量作为耦合。一个质量牛顿中介体则传递$1/r^{3}$的力；一个绝热不变量将这两条定律追溯到中介体的色散关系。当延续到负中介体能量时，闭式解变为三角函数形式，束缚了一个一维的库仑原子的力学类比。
英文摘要
We solve in closed form a one-dimensional relativistic system: two masses interacting only through elastic collisions with a massless mediator bouncing between them. Momenta, times, and positions are hyperbolic functions of the collision index. The mediator energy, interpreted as the pair's effective potential, obeys an exact discrete Coulomb law, $V\propto 1/r$, with a Lorentz-invariant action as coupling. A massive Newtonian mediator instead transmits a $1/r^{3}$ force; one adiabatic invariant traces both laws to the mediator's dispersion relation. Continued to negative mediator energy, the closed forms turn trigonometric, binding a one-dimensional mechanical analog of the Coulomb atom.
发表机构
- Massachusetts Institute of Technology（麻省理工学院）
- Korea Military Academy（韩国军事学院）
- Korea University（韩国大学）
机构由 AI 辅助整理，请以论文原文为准。
