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We study the dynamics of a quantum heavy particle undergoing a repulsiveinteraction with a light one. The main motivation is the detailed descriptionof the loss of coherence induced on a quantum system (in our model, the heavyparticle) by the interaction with the environment (the light particle). Thecontent of the paper is analytical and numerical. Concerning the analyticalcontribution, we show that an approximate description of the dynamics of theheavy particle can be carried out in two steps: first comes the interaction,then the free evolution. In particular, all effects of the interaction can beembodied in the action of a collision operator that acts on the initial stateof the heavy particle. With respect to previous analytical results on the sametopics, we turn our focus from the M{\o}ller wave operator to the fullscattering operator, whose analysis proves to be simpler. Concerning thenumerical contribution, we exploit the previous analysis to construct anefficient numerical scheme that turns the original, multiscale, two-bodyproblem in two one-body problems which can be solved separately. This leads toa considerable gain in simulation time. We present and interpret somesimulations carried out on specific one-dimensional systems by using the newscheme. Finally, we propose a new description of the mechanism of decoherenceinduced by scattering: decoherence is produced by an interference-free bumpwhich arises from the initial state of the heavy particle immediately after thecollision. We support such a picture by numerical evidence as well as by anapproximation theorem.

De coherence for a heavy particle interacting with a light one: new analysis and numerics