Stochastic Maxwell-Lorentz equation in radiation damping

Abstract

Radiation damping of an accelerated particle coupled with the field is a classical problem. Still there are difficulties. Time symmetry is broken. So the radiation damping belongs to a class of phenomena that includes transport properties. In a series of our recent articles we proposed a radically new approach based on the extension of the dynamics of integrable systems. There, we considered a simple model: a harmonic oscillator interacting with a field. For integrable systems, it is well known that there exists a unitary transformation U. However, in the radiation damping we have resonances between the action of a charged particle and the actions of the field modes. This makes the system an example of Poincaré nonintegrable systems. We extended the unitary operator to a nonunitary operator Λ. This changes the dynamical description of radiation damping. Once we know the Hamiltonian, we can write the Hamilton equations. But we have the opportunity to go to new descriptions. The invertible Λ transformation gives many new aspects, which are hidden in the initial description. For example, we showed that there are fluctuations in the emitted field. In the current article we apply the Λ transformation to describe the evolution of the emitted field from the charged particle and show that the fluctuations lead to a Langevin equation for the field modes. As a consequence, we have a stochastic wave equation that is an extension of Maxwell-Lorentz equation for classical matter-field interacting systems. © 2004 Wiley Periodicals, Inc.