  We investigate a mean-field approach to a quantum brownian particle
interacting with a quantum thermal bath at temperature $T$, and subjected to a
non-linear potential. An exact, partially classical description of quantum
brownian motion is proposed, which uses negative probabilities in its
intermediate steps. It is shown that properties of the quantum particle can be
mapped to those of two classical brownian particles in a common potential,
where one of them interacts with the quantum bath, whereas another one
interacts with a classical bath at zero temperature. Due to damping the system
allows a unique and non-singular classical limit at $\hbar \to 0$. For high $T$
the stationary state becomes explicitly classical. The low-temperature case is
studied through an effective Fokker-Planck equation. Non-trivial purely quantum
correlation effects between the two particles are found.
