Reduction of order, resummation and radiation reaction
Abstract
The Landau-Lifshitz equation is the first in an infinite series of approximations to the Lorentz-Abraham-Dirac equation obtained from `reduction of order'. We show that this series is divergent, predicting wildly different dynamics at successive perturbative orders. Iterating reduction of order ad infinitum in a constant crossed field, we obtain an equation of motion which is free of the erratic behaviour of perturbation theory. We show that Borel-Pad\'e resummation of the divergent series accurately reproduces the dynamics of this equation, using as little as two perturbative coefficients. Comparing with the Lorentz-Abraham-Dirac equation, our results show that for large times the optimal order of truncation typically amounts to using the Landau-Lifshitz equation, but that this fails to capture the resummed dynamics over short times.
Keywords
Cite
@article{arxiv.2105.01640,
title = {Reduction of order, resummation and radiation reaction},
author = {Robin Ekman and Tom Heinzl and Anton Ilderton},
journal= {arXiv preprint arXiv:2105.01640},
year = {2021}
}