Extracting the Geometric Phase from the Ensemble of Trajectories

Traditionally, methods designed to investigate the effects of the geometric phase in reaction dynamics, such as including a vector potential in the nuclear Hamiltonian, necessitate the explicit manipulation of geometric phase-related terms in the adiabatic representation. In contrast, the diabatic representation provides an alternative approach that implicitly addresses the geometric phase and nonadiabatic issues. In this study, we present a method to directly extract the phase information on the geometric phase from the ensemble of interdependent trajectories utilizing the diabatic representation. This approach presents a direct means of quantitatively examining the geometric phase effects in dynamics and has the potential to yield observables suitable for experimental measurement.