A particle across a medium: How decoherence relates to the index of refraction

We deduce from a microscopic point of view the equation that describes how the state of a particle crossing a medium decoheres. We find out that the part of the density matrix that evolves preserving coherence, is fully described with the index of refraction. Its imaginary part has the origin in the Lindblad operators, which are the responsible of decoherence. We apply our results to the example of a particle crossing a gas: we find a master equation of the Lindblad type, and compute explicitly the Lindblad operators in terms of the interaction potential between the particle and a target of the medium. Two limit situations are treated: when the particle is much heavier than the targets of the medium and vice versa.