  We study low-energy dynamics generated by a two-dimensional two-state
Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum
wavepacket and trajectories dynamics. Recently, these dynamics were studied by
comparing the adiabatic representation and the exact factorization, with the
purpose to highlight the different nature of topological- and geometric-phase
effects arising in the two theoretical representation of the same problem.
Here, we employ the exact factorization to understand how to model accurately
low-energy dynamics in the vicinity of a conical intersection using an
approximate description of the nuclear motion that uses trajectories. We find
that, since nonadiabatic effects are weak but non-negligible, the
trajectory-based description that invokes the classical approximation struggles
to capture the correct behavior.
