  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
behavior 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.

Quantum Physics