26 research outputs found
Radiative Damping and Functional Differential Equations
We propose a general technique to solve the classical many-body problem with
radiative damping. We modify the short-distance structure of Maxwell
electrodynamics. This allows us to avoid runaway solutions as if we had a
covariant model of extended particles. The resulting equations of motion are
functional differential equations (FDEs) rather than ordinary differential
equations. Using recently developed numerical techniques for stiff FDEs, we
solve these equations for the one-body central force problem with radiative
damping with a view to benchmark our new approach. Our results indicate that
locally the magnitude of radiation damping may be well approximated by the
standard third-order expression but the global properties of our solutions are
dramatically different. We comment on the two body problem and applications to
quantum field theory and quantum mechanics.Comment: (v1) 6 pages, version of Nov 22, 2007 (v2) 24 pages double-spaced.
calculations and results unchanged, explanations elaborate
Introduction to the theory and application of differential equations with deviating arguments
A Weyl-geodesic field of cones in a three-dimensional Riemannian space II. First integrals of geodesics
First-passage times for non-Markovian processes: Shot noise
The stochastic-trajectory-analysis technique is applied to the calculation of the meanÂżfirst-passage-time statistics for processes driven by external shot noise. Explicit analytical expressions are obtained for free and bound processes