Solvable kinetic Gaussian model in an external field

In this paper, the single-spin transition dynamics is used to investigate t he kinetic Gaussian model in a periodic external field. We first derive the fundamental dynamic equations, and then treat an isotropic d-dimensional h ypercubic lattice Gaussian spin system with Fourier's transformation method . We obtain exactly the local magnetization and the equal-time pair-correla tion function. The critical characteristics of the dynamical relaxation tau (q), the complex susceptibility chi(w,q), and the dynamical response are di scussed. The results show that the time evolution of the dynamical quantiti es and the dynamical responses of the system strongly depend on the frequen cy and the wave vector of the external field.