Phase space theory of quantum–classical systems with nonlinear and stochastic dynamics

A novel theory of hybrid quantum–classical systems is developed, utilizing the mathematical framework of constrained dynamical systems on the quantum–classical phase space. Both, the quantum and classical descriptions of the respective parts of the hybrid system are treated as fundamental. Therefore, the description of the quantum–classical interaction has to be postulated, and includes the effects of neglected degrees of freedom. Dynamical law of the theory is given in terms of nonlinear stochastic differential equations with Hamiltonian and gradient terms. The theory provides a successful dynamical description of the collapse during quantum measurement. •A novel theory of quantum–classical systems is developed.•Framework of quantum constrained dynamical systems is used.•A dynamical description of the measurement induced collapse is obtained.