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Examples: (1) https://iopscience.iop.org/article/10.1088/1742-6596/442/1/012006.

(2) https://arxiv.org/abs/1802.04787

However, they tend to focus more on theoretical aspects (consistency, existence of generalized brackets and/or joint Hamiltonian/unitary evolution) and less on application to real systems. I guess, hybrid theories are supposed to give a good approximation in mesoscopic systems, where some things are big enough to be considered classical but not that big that all quantum effects can be ignored.

So, is there an actual physical systems (not toy models) where quantum-classical theories give good results for practical calculations?