Lorentz-Dirac方程的临界流形
The critical manifold of the Lorentz-Dirac equation
摘要：
我们研究了Lorentz-Dirac方程的解，证明了它的解流具有与临界现象中的重整化群流相同的结构.洛伦兹-狄拉克方程的物理解位于临界面上。临界表面是排斥的，即任何轻微的偏离都会被放大，结果解决方案会走向无穷大。另一方面，狄拉克的渐近条件（加速度长时间为零）迫使解位于临界流形上。临界面可以用微扰法确定。从而得到一个有效的二阶方程，我们将其应用于各种情况，特别是电子在潘宁陷阱中的运动。
英文摘要：
We investigate the solutions to the Lorentz-Dirac equation and show that its solution flow has a structure identical to the one of renormalization group flows in critical phenomena. The physical solutions of the Lorentz-Dirac equation lie on the critical surface. The critical surface is repelling, i.e. any slight deviation from it is amplified and as a result the solution runs away to infinity. On the other hand, Dirac's asymptotic condition (acceleration vanishes for long times) forces the solution to be on the critical manifold. The critical surface can be determined perturbatively. Thereby one obtains an effective second order equation, which we apply to various cases, in particular to the motion of an electron in a Penning trap.
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