Numerical study of electromagnetic two-body problem and multiple scale method

Abstract

In this project I shall study the dynamics of the electromagnetic two-body problem numerically. The stay in Italy will greatly benefit the development of my project 2005/03046-5. As explained in the project, the equations of motion for this dynamical system are stiff delay equations that are highly non-trivial to integrate. I chose to spend some months to collaborate with specialists on this type of numerical work, as explained in the project. In the present year of 2006 I published a long paper with a qualitative analysis of this dynamics, Phys. Rev. E 73, 022626 (2006). The electromagnetic two-body problem in Dirac’s theory has a nontrivial dynamics because of the self-interaction and the delay in the equations of motion. Because of the delay, the dynamics in the neighborhood of circular orbits displays a motion in a fast timescale superposed to the slow circular motion. I have started to investigate the consequences of balancing this fast dynamics in the neighborhood of circular orbits. This balancing of the fast dynamics predicts results in the atomic scale and in qualitative and quantitative agreement with the results of quantum electrodynamics (QED); The orbits are parameterized by an integer and the angular momenta are approximate multiples of a fundamental angular momentum of the order of Planck’s constant. In this project I am also going to work on a detailed multiscale method of solution for this dynamics, one that starts from the fast dynamics. (AU)