It should be noted that the approach outlined here is one of many realizations for spin-mapping dynamics. In this work, we focus on the so-called spin-mapping dynamics confined to the W-sphere, which shows the most accurate results for the widest variety of systems. The correlation function for the time-evolved density matrix ρ αn,β m , given an initial excitation to state arbitrary state σl (i.e., Â = |σl ⟩ ⟨σl | in Eq. 48) is evaluated using focused initial conditions such that,