De Luca Jayme
Departamento de Física, Universidade Federal de São Carlos, Rodovia Washington Luis, km 235 Caixa Postal 676, São Carlos, São Paulo, Brazil 13565-905.
Phys Rev E Stat Nonlin Soft Matter Phys. 2005 May;71(5 Pt 2):056210. doi: 10.1103/PhysRevE.71.056210. Epub 2005 May 24.
We introduce an ad hoc electrodynamics with advanced and retarded Liénard-Wiechert interactions plus the dissipative Lorentz-Dirac self-interaction force. We study the covariant dynamical system of the electromagnetic two-body problem, i.e., the hydrogen atom. We perform the linear stability analysis of circular orbits for oscillations perpendicular to the orbital plane. In particular, we study the normal modes of the linearized dynamics that have an arbitrarily large imaginary eigenvalue. These large eigenvalues are fast frequencies that introduce a fast (stiff) time scale into the dynamics. As an application, we study the phenomenon of resonant dissipation, i.e., a motion where both particles recoil together in a drifting circular orbit (a bound state), while the atom dissipates center-of-mass energy only. This balancing of the stiff dynamics is established by the existence of a quartic resonant constant that locks the dynamics to the neighborhood of the recoiling circular orbit. The resonance condition quantizes the angular momenta in reasonable agreement with the Bohr atom. The principal result is that the emission lines of quantum electrodynamics agree with the prediction of our resonance condition within 1% average deviation.
我们引入一种特殊的电动力学，它包含超前和延迟的李纳-维谢尔相互作用以及耗散的洛伦兹-狄拉克自相互作用力。我们研究电磁两体问题，即氢原子的协变动力学系统。我们对垂直于轨道平面的振荡进行圆形轨道的线性稳定性分析。特别地，我们研究线性化动力学的具有任意大虚特征值的正常模式。这些大特征值是快速频率，它们将一个快速（刚性）时间尺度引入到动力学中。作为一个应用，我们研究共振耗散现象，即一种运动，其中两个粒子在漂移的圆形轨道（束缚态）中一起反冲，而原子仅耗散质心能量。这种刚性动力学的平衡是由一个四次共振常数的存在建立的，该常数将动力学锁定在反冲圆形轨道的邻域。共振条件使角动量量子化，与玻尔原子相当吻合。主要结果是，量子电动力学的发射线与我们共振条件的预测在平均偏差1%以内相符。
