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

TL;DR

This paper investigates a coupled oscillator-spin system to compare quantum, classical, and semi-classical dynamics, revealing that semi-classical backreaction models may not adequately bridge quantum gravity and curved spacetime theories.

Contribution

It introduces a detailed model comparing quantum, classical, and semi-classical dynamics, highlighting limitations of semi-classical backreaction in intermediate regimes.

Findings

Entangled states lead to unique oscillator trajectories.

Quantum and classical models agree at weak couplings.

Deviations occur at intermediate couplings.

Abstract

Motivated by quantum gravity, semi-classical 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 nonperturbative calculations of oscillator and entanglement entropy dynamics, we find that entangled tripartite states produce novel oscillator trajectories, and that 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 back reaction does not provide a suitable intermediate regime between quantum gravity and quantum theory on curved spacetime.