Koopman wavefunctions and classical states in hybrid quantum–classical dynamics

We deal with the reversible dynamics of coupled quantum and classical systems. Based on a recent proposal by authors, we exploit theory hybrid quantum–classical wavefunctions to devise closure model for in which both density matrix Liouville distribution retain their initial positive sign. In this way, evolution allows identifying state interaction at all times, thereby addressing series stringent consistency requirements. After combining Koopman's Hilbert-space method mechanics van Hove's unitary representations prequantum theory, is made available variational structure underlying suitable wavefunction factorization. Also, use Poisson reduction symmetry show that possesses noncanonical does not seem have appeared before. As an example, specialized case two-level