Semiclassical Approach to Self-Consistent Classical-Quantum Coupling*

A self-consistent coupling of classical and quantum subsystems that correctly predicts backreaction effects is derived for the first time by considering a bipartite quantum system and taking the semiclassical large quantum number limit for one of the subsystems. This approach results in a configuration space version of the Koopman-van Hove Hamiltonian [1-3] for the coupled system and is equivalent to an operator-valued version of WKB theory.  Injecting the configuration space dynamics into classical phase space yields a straightforward proof of the recently proposed methodology in [1]. However, the semiclassical version has different boundary conditions than the classical version that improve accuracy by generating "quantum" effects such as interference, the Einstein-Brillouin-Keller quantization conditions, and tunneling through classically forbidden regions.  While the configuration space version is nonlinear, the phase space version is both linear and unitary which enables the possibility of simulating semiclassical dynamics on quantum computers.