Finally, in Fig. , we compare the long-time dynamics up to 1 ps in the isolated 2D model and in the system+bath model by analyzing the nuclear kinetic energy as function of time along the reactive coordinate ϕ (left panels) and along the coupling mode q (right panels) using CT-TSH (upper panels) and TSH-ED (lower panels). While the inclusion of the environment does not strongly affect the behavior of the system along ϕ, we observe a striking damping of the nuclear kinetic energy along the high-frequency coupling mode q due to the bath of harmonic oscillators. The effect is severe when the dynamics is simulated with CT-TSH, but it is not negligible even with TSH-ED, and shows once again that the presence of the environment tends to reduce the differences in dynamics simulated with the two trajectory-based methods.