where R i represents the vector containing position coordinates of all excitons for the i th trajectory (not to be confused with the nuclear DOF R n,ν , as we used a shorthand notation for R = {R n,ν }). Similarly, we can collect the momentum coordinates from the "m" trajectories to construct the batch matrix, {P } m . These {R} m and {P } m can be collectively propagated using the simple forms of Eq. 8a and Eq. 8b.