Scattering asymptotics for a charged particle coupled to the Maxwell field

@article{Imaykin2011ScatteringAF,
  title={Scattering asymptotics for a charged particle coupled to the Maxwell field},
  author={Valery Imaykin and Alexander Komech and Herbert Spohn},
  journal={Journal of Mathematical Physics},
  year={2011},
  volume={52},
  pages={042701-042701}
}
We establish long time soliton asymptotics for the nonlinear system of Maxwell equations coupled to a charged particle. The coupled system has a six-dimensional manifold of soliton solutions. We show that in the long time approximation, any solution, with an initial state close to the solitary manifold, is a sum of a soliton and a dispersive wave which is a solution of the free Maxwell equations. It is assumed that the charge density satisfies the Wiener condition. The proof further develops… 
Asymptotic stability of stationary states in the wave equation coupled to a nonrelativistic particle
We consider the Hamiltonian system consisting of a scalar wave field and a single particle coupled in a translation invariant manner. The point particle is subjected to an external potential. The
Soliton asymptotics for systems of `field-particle' type
This survey is devoted to the recent mathematical progress in the study of interaction between particles and fields. It covers a series of papers from 2000 till now. Three systems describing the
Symplectic projection methods of deriving long-time asymptotics for nonlinear PDEs
We consider some systems which describe a field-particle interaction, namely a charged particle coupled to the scalar wave field, to the Klein-Gordon field, and to the Maxwell field. Since the
Asymptotic stability of solitons for nonlinear hyperbolic equations
Fundamental results on asymptotic stability of solitons are surveyed, methods for proving asymptotic stability are illustrated based on the example of a nonlinear relativistic wave equation with
Stability of Solitons for a Rotating Charge with a Fixed Center of Mass in the Maxwell Field
We consider the system of Maxwell equations and Lorentz torque equation which describes the motion of a charge in an electromagnetic field. Under certain symmetry conditions on the charge
Global solution of the electromagnetic field-particle system of equations
In this paper we discuss global existence of the solution of the Maxwell and Newton system of equations, describing the interaction of a rigid charge distribution with the electromagnetic field it
Attractors of Hamilton nonlinear PDEs
This is a survey of results on long time behavior and attractors for Hamiltonian nonlinear partial differential equations, considering the global attraction to stationary states, stationary orbits,
Towards a derivation of Classical ElectroDynamics of charges and fields from QED
. The purpose of this article is twofold: • On one hand, we rigorously derive the Newton–Maxwell equation in the Coulomb gauge from first principles of quantum electrodynamics in agreement with the
Radiative damping: a case study
We are interested in the motion of a classical charge coupled to the Maxwell self-field and subject to a uniform external magnetic field, B. This is a physically relevant, but difficult dynamical
A note on the infrared problem in model field theories
In this note we critically re-examine the usual procedure of quantization of classical wave equations with static sources. We point out that the origin of infrared difficulties in the so called van
...
...

References

SHOWING 1-10 OF 29 REFERENCES
Scattering of solitons for coupled wave-particle equations
On Scattering of Solitons for the Klein–Gordon Equation Coupled to a Particle
We establish the long time soliton asymptotics for the translation invariant nonlinear system consisting of the Klein–Gordon equation coupled to a charged relativistic particle. The coupled system
Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit
Abstract.We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite
Long—time asymptotics for the coupled maxwell—lorentz equations
We determine the long time behavior of solutions to the Maxwell-Lorentz equations, which describe a charge coupled to the electromagnetic eld and subject to external time-independent potentials. The
Soliton-Type Asymptotics for the Coupled Maxwell-Lorentz Equations
Abstract.We consider a Maxwell field translation invariantly coupled to a single charge. This Hamiltonian system admits soliton-type solutions, where the charge and the co-moving field travel with
Nonlinear scattering: The states which are close to a soliton
We assume that the nonlinear Schroedinger equation with sufficiently general nonlinearity admits solutions of the soliton type. The Cauchy problem with initial data close to a soliton is considered.
Scattering of solitons of the Klein–Gordon equation coupled to a classical particle
Long-time asymptotics are established for finite energy solutions of the scalar Klein–Gordon equation coupled to a relativistic classical particle: any “scattering” solution is asymptotically a sum
SCATTERING THEORY FOR A PARTICLE COUPLED TO A SCALAR FIELD
We establish soliton-like asymptotics for finite energy solutions to classical particle coupled to a scalar wave field. Any solution that goes to infinity as $t\to\infty$ converges to a sum of
Effective Dynamics for a Mechanical Particle Coupled to a Wave Field
We consider a particle coupled to a scalar wave field and subject to the slowly varying potential V ("q) with small ". We prove that if the initial state is close, order " 2 , to a soliton (=dressed
...
...