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Rigorous derivation of Lindblad equations from quantum jumps processes in 1D

We are interested by the behaviour of a 1D single heavy particle, interacting with an environment made of very fast particles in a thermal state. Assuming that the interactions are instantaneous, we construct an appropriate quantum jump process for the density operator of the heavy particle. In a weak-coupling limit (many interactions with few effect), we show that the solutions of jump process converge in law in the appropriate space towards the solution of a Lindbald master equation. To the best of our knowledge, it seems to be the first rigorous derivation of a dissipative quantum evolution equation.