Hybrid quantum-classical dynamics of pure-dephasing systems ^*

We consider the interaction dynamics of a classical oscillator and quantum two-level system for different pure-dephasing Hamiltonians type $\widehat{H}(q,p)=H_C(q,p)\boldsymbol{1}+H_I(q,p)\widehat\sigma_z$. This systems represents severe challenge popular hybrid quantum-classical descriptions. For example, in case common Ehrenfest model, density evolution is shown to decouple entirely from dynamics. focus on recently proposed wave equation that based Koopman's wavefunction description mechanics. model retains correlations whenever coupling potential present. Here, several benchmark problems are considered results compared with those arising fully A good agreement found series study cases involving harmonic oscillators linear quadratic coupling, as well time-varying parameters. In all these coincides exactly resulting description. special time-independent varying frequency, Bloch rotation exhibits peculiar features escape addition, nonlinear corrections Hamiltonian lead an overall growth decoherence at long times, which absent treatment.