Stiff stability of the hydrogen atom in dissipative Fokker electrodynamics.
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.
De Luca
Jayme
J
Departamento de Física, Universidade Federal de São Carlos, Rodovia Washington Luis, km 235 Caixa Postal 676, São Carlos, São Paulo, Brazil 13565-905. deluca@df.ufscar.br