  We consider the Hamiltonian system of scalar wave field and a single
nonrelativistic particle coupled in a translation invariant manner. The
particle is also 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 ${\cal S}$ of all stationary states in the long time limit $t\to\pm\infty$.
Further we show that the rate of relaxation to a stable stationary state is
determined by spatial decay of initial data. The convergence is followed by the
radiation of the dispersion wave which is a solution to the free wave equation.
  Similar relaxation has been proved previously for the case of relativistic
particle when the speed of the particle is less than the speed of light. Now we
extend these results to nonrelativistic particle with arbitrary superlight
velocity. However, we restrict ourselves by the plane particle trajectories.
The extension to general case remains an open problem.
