  Semiclassical path integral expression for a quantum system coupled to a
harmonic bath is derived based on the stationary phase condition. It is
discovered that the system path is non-Markovian. Most strikingly, the system
path not only couples to its past (as in the Langevin equation), but also to
its future, i.e. the equation of motion for the system is an
integro-differential equation that involves all times. Numerical tests are
performed to confirm that the future-involved term is indeed necessary. Because
of the future-non-Markovian nature of the equation, the numerical solution
cannot be obtained by iterative methods. Instead, root search algorithms must
be employed.
