  We propose a system of equations to describe the interaction of a
quasiclassical variable $X$ with a set of quantum variables $x$ that goes
beyond the usual mean field approximation. The idea is to regard the quantum
system as continuously and imprecisely measured by the classical system. The
effective equations of motion for the classical system therefore consist of
treating the quantum variable $x$ as a stochastic c-number $\x (t) $ the
probability distibution for which is given by the theory of continuous quantum
measurements. The resulting theory is similar to the usual mean field equations
(in which $x$ is replaced by its quantum expectation value) but with two
differences: a noise term, and more importantly, the state of the quantum
subsystem evolves according to the stochastic non-linear Schrodinger equation
of a continuously measured system. In the case in which the quantum system
starts out in a superposition of well-separated localized states, the classical
system goes into a statistical mixture of trajectories, one trajectory for each
individual localized state.
