Résumé:

Based on the de Broglie-Bohm formulation of quantum mechanics, quantum trajectories have seen a growing interest in the chemical dynamics community over the past ten years or so. As the name suggests, quantum trajectories (QTs), are able to capture quantum dynamical effects---tunneling, in particular---which are known or suspected to be important for many processes of current interest: tunneling effect in reactive processes (in gas or condensed phases), non-adiabatic effects, quantum coherence, proton transfers in biochemistry, \ldots. Originally considered an interpretative tool for quantum mechanics, QTs have been recently rediscovered as a computational method for doing quantum reaction dynamics. Traditionally, analytic quantum trajectories, often used as an interpretative tool, were extracted from conventional wave packets. In the more recent synthetic quantum trajectory methods, both the trajectories and the wave function are computed on the fly, each affecting the propagation of the other. We recently investigate the most recent formulation of QTs proposed by Bill Poirier and coworkers, which regards the trajectory ensemble itself as the fundamental quantum state entity, rather than the wavefunction. Similarly to classical trajectories, QTs obey Hamiltonian equations of motion, albeit special ones. The resultant quantum trajectory simulation scheme so obtained is identical to a classical trajectory simulation, apart from the addition of one extra "quantum'' coordinate. Using standard techniques to integrate the equations of motion, quantum trajectory simulations is indeed capable of providing accurate quantum dynamical information, but with the same ease-use and computational effort as classical trajectory simulation. In this QTs formulation, a $4^\mathrm{th}$-order Newtonian-like ordinary differential equation (ODE) was derived that describes 1D stationary scattering states exactly, solely in terms of quantum trajectories. The concept of those QTs will be presented and illustrated by our application for a 1D Eckart barrier system as well as its application in a capture model of the cold and ultra-cold Li + CaH reaction. Some perpectives will also presented on the way to perform quantum-classical trajectories simulations for chemical reaction involving many degree of freedom (high dimensional reaction dynamics).