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

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