Abstract:
We consider a particle coupled to a scalar wave field and subject to the slowly varying potential V(ɛq) with small ɛ. We prove that if the initial state is close, order ɛ2, 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 ɛ−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(ɛq) with energy-momentum relation E(P).
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Received: 2 September 1998 / Accepted: 13 November 1998
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ID="*"Supported partly by French–Russian A.M.Liapunov Center of Moscow State University, by Max-Planck Institute for Mathematics in the Sciences (Leipzig), and by research grants of INTAS (IR-97-113) and of Volkswagen-Stiftung.
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ID="**"Supported by DAAD andNSF (throuhg a grant of Ch. Jones) during a stay at Brown University <AU><FNMS>Herbert<SNM>Spohn<ORF RID="a3"
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KomechRID="*"ID="*"Supported partly by French–Russian A.M.Liapunov Center of Moscow State University, by Max-Planck Institute for Mathematics in the Sciences (Leipzig), and by research grants of INTAS (IR-97-113) and of Volkswagen-Stiftung., A., KunzeRID="**"ID="**"Supported by DAAD andNSF (throuhg a grant of Ch. Jones) during a stay at Brown University <AU><FNMS>Herbert<SNM>Spohn<ORF RID="a3", M. Effective Dynamics for a Mechanical Particle Coupled to a Wave Field. Comm Math Phys 203, 1–19 (1999). https://doi.org/10.1007/s002200050023
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DOI: https://doi.org/10.1007/s002200050023