  The phase-space path-integral approach to the damped harmonic oscillator is
analyzed beyond the Markovian approximation. It is found that pairs of
nonclassical trajectories contribute to the path-integral representation of the
Wigner propagating function. Due to the linearity of the problem, the sum
coordinate of a pair still satisfies the classical equation of motion.
Furthermore, it is shown that the broadening of the Wigner propagating function
of the damped oscillator arises due to the time-nonlocal interaction mediated
by the heat bath.
