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We consider the Hamiltonian system consisting of scalar wave field and asingle particle coupled in a translation invariant manner. The point particleis subject to an external potential. The stationary solutions of the system area Coulomb type wave field centered at those particle positions for which theexternal force vanishes. It is assumed that the charge density satisfies theWiener condition which is a version of the "Fermi Golden Rule". We prove thatin the large time approximation any finite energy solution, with the initialstate close to the some stable stationary solution, is a sum of this stationarysolution and a dispersive wave which is a solution of the free wave equation.

Asymptotic stability of stationary states in wave equation coupled to nonrelativistic particle