Komech A., Spohn H., Kunze M.
Long-Time Asymptotics for a Classical Particle
Interacting with a Scalar Wave Field
(72K, Latex)
ABSTRACT. We consider the Hamiltonian system consisting of scalar
wave field and a single particle coupled in a translation
invariant manner. The point particle is subject to a
confining external potential. The stationary solutions of
the system are a Coulomb type wave field centered at those
particle positions for which the external force vanishes.
We prove that solutions of finite energy converge, in
suitable local energy seminorms, to the set of stationary
solutions in the long time limit $t\to\pm\infty$. The rate
of relaxation to a stable stationary solution is determined
by spatial decay of initial data.