Long - Time Asymptotics for a Classical ParticleInteracting with a Scalar Wave Field
نویسندگان
چکیده
We consider the Hamiltonian system consisting of scalar wave eld and a single particle coupled in a translation invariant manner. The point particle is subject to a connning external potential. The stationary solutions of the system are a Coulomb type wave eld centered at those particle positions for which the external force vanishes. We prove that solutions of nite energy converge, in suitable local energy seminorms, to the set of stationary solutions in the long time limit t ! 1. The rate of relaxation to a stable stationary solution is determined by spatial decay of initial data.
منابع مشابه
Soliton - Like Asymptotics for a Classical ParticleInteracting with a Scalar Wave Field
Interacting with a Scalar Wave Field Alexander Komech1 Department of Mechanics and Mathematics of Moscow State University, Moscow 119899, Russia email: [email protected] Herbert Spohn Theoretische Physik, Ludwig-Maximilians-Universit at Theresienstrasse 37, D-80333 M unchen, Germany email: [email protected] AbstractWe consider a scalar wave eld translation invariantly coupl...
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