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

Nonclassical phase-space trajectories for the damped harmonic quantum oscillator