Effective Dynamics for a Mechanical Particle Coupled to a Wave Field
Abstract
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 particle), then the solution stays forever close to the soliton manifold. This estimate implies that over a time span of order ∊^{2} the radiation losses are negligible and that the motion of the particle is governed by the effective Hamiltonian H_{eff}(q,P)=E(P)+V(∊q) with energymomentum relation E(P).
 Publication:

Communications in Mathematical Physics
 Pub Date:
 1999
 DOI:
 10.1007/s002200050023
 Bibcode:
 1999CMaPh.203....1K