Equation of motion of a driven spin coupled to a bath

The equation of motion of an arbitrarily driven spin linearly coupled to a bosonic bath is derived with the help of path integral techniques. The nonlocal-in-time interaction in the influence function is converted by means of a Hubbard transformation to give rise to a Gaussian random field. The average over this field is performed using a series expansion to obtain the equation of motion in closed form. The weak coupling limit is discussed with an example. A partial summation procedure of the series expansion is applied to a relaxation process.