García Moreno, GerardoAres Santos, LauraLuis Aina, Alfredo2023-06-162023-06-162019-120003-491610.1016/j.aop.2019.167961https://hdl.handle.net/20.500.14352/6009© 2019 Elsevier Inc. A.L. and L.A. acknowledge financial support from Spanish Ministerio de Economía y Competitividad Projects No, FIS2016-75199-P, and from the Comunidad Autónoma de Madrid research consortium QUITEMAD+ Grant No. S2013/ICE-2801.; L.A. acknowledges financial support from European Social Fund and the Spanish Ministerio de Ciencia Innovación y Universidades Contract Grant No. BES-2017-081942.In this work we provide a complete model of semiclassical theories by including back-reaction and correlation into the picture. We specially aim at the interaction between light and a two-level atom, and we also illustrate it via the coupling of two harmonic oscillators. Quantum and classical systems are treated on the same grounds via the Wigner-Weyl phase-space correspondence of the quantum theory. We show that this model provides a suitable mixture of the quantum and classical degrees of freedom, including the fact that the evolution transfers nonclassical features to the classical subsystem and nonquantum behaviour to the quantum subsystem. In that sense, we can no longer distinguish between classical and quantum variables and we need to talk about a hybrid model. (C) 2019 Elsevier Inc. All rights reserved.spajournal articlehttp://dx.doi.org/10.1016/j.aop.2019.167961https://www.sciencedirect.comopen access535DecoherenceRepresentationPhysicsCavityÓptica (Física)2209.19 Óptica Física