In Fig. , we analyze the effect of the coupling between the system and the bath in the 2D + 2BM simulation. From the expression of the Hamiltonian given in Eq. ( ), it is clear that there is no direct coupling between the modes of the system ϕ, q and the modes of the bath {x j }. However, the bath affects the energies of the electronic states in different ways (see Eq. ( )), and thus, due to the nonadiabatic electron-nuclear coupling within the system, correlation is established along the dynamics between the nuclear degrees of freedom of the system and the bath degrees of freedom.