Coupling Classical and Quantum Variables using Continuous Quantum Measurement Theory

Continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable X with a quantum variable x, where the quasiclassical nature of X is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic nonlinear Schr\"odinger equation of a continuously measured system, and the classical system couples to a stochastic c number x̄(t) representing the imprecisely measured value of x. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states.