  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.
