Dynamics and entanglement in quantum and quantum-classical systems: lessons for gravity*

Motivated by quantum gravity, semiclassical theory, and quantum theory on curved spacetimes, we study the system of an oscillator coupled to two spin-1/2 particles. This model provides a prototype for comparing three types of dynamics: the full quantum theory, the classical oscillator with spin backreaction, and spins propagating on a fixed oscillator background. From calculations of oscillator and entanglement entropy evolution, we find the three systems give equivalent dynamics for sufficiently weak oscillator-spin couplings but deviate significantly for intermediate couplings. These results suggest that semiclassical dynamics with backreaction does not provide a suitable intermediate regime between quantum gravity and quantum theory on curved spacetime.