Semiclassical backreaction: A qualitative assessment

The backreaction of quantum degrees of freedom on classical backgrounds is a poorly understood topic in theoretical physics. Most often it is treated within the semiclassical approximation with the help of various prescriptions accounting for the effect of quantum excitations on the dynamics of the background. We focus on two popular ones: (i) the mean-field approximation whereby quantum degrees of freedom couple to the classical background via their quantum expectation values; (ii) the (stochastic) method whereby the fully coupled system is evolved using classical equations of motion for various randomly sampled initial conditions of the quantum degree of freedom, and a statistical average is performed . We evaluate the performance of each method in a simple toy model against a fully quantum mechanical treatment, and identify its regime of validity. We interpret the results in terms of quantum entanglement and loss of classicality of the background.