  In order to alleviate the computational costs of fully quantum nonadiabatic
dynamics, we present a mixed quantum-classical (MQC) particle method based on
the theory of Koopman wavefunctions. Although conventional MQC models often
suffer from consistency issues such as the violation of Heisenberg's principle,
we overcame these difficulties by blending Koopman's classical mechanics on
Hilbert spaces with methods in symplectic geometry. The resulting continuum
model enjoys both a variational and a Hamiltonian structure, while its
nonlinear character calls for suitable closures. Benefiting from the underlying
action principle, here we apply a regularization technique previously developed
within our team. This step allows for a singular solution ansatz which
introduces the trajectories of computational particles - the koopmons -
sampling the Lagrangian classical paths in phase space. In the case of Tully's
nonadiabatic problems, the method reproduces the results of fully quantum
simulations with levels of accuracy that are not achieved by standard MQC
Ehrenfest simulations. In addition, the koopmon method is computationally
advantageous over similar fully quantum approaches, which are also considered
in our study. As a further step, we probe the limits of the method by
considering the Rabi problem in both the ultrastrong and the deep strong
coupling regimes, where MQC treatments appear hardly applicable. In this case,
the method succeeds in reproducing parts of the fully quantum results.
