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We develop a Monte Carlo wave function algorithm for the quantum linearBoltzmann equation, a Markovian master equation describing the quantum motionof a test particle interacting with the particles of an environmentalbackground gas. The algorithm leads to a numerically efficient stochasticsimulation procedure for the most general form of this integro-differentialequation, which involves a five-dimensional integral over microscopicallydefined scattering amplitudes that account for the gas interactions in anon-perturbative fashion. The simulation technique is used to assess variouslimiting forms of the quantum linear Boltzmann equation, such as the limits ofpure collisional decoherence and quantum Brownian motion, the Bornapproximation and the classical limit. Moreover, we extend the method to allowfor the simulation of the dissipative and decohering dynamics of superpositionsof spatially localized wave packets, which enables the study of many physicallyrelevant quantum phenomena, occurring e.g. in the interferometry of massiveparticles.

Stochastic simulation algorithm for the quantum linear Boltzmann equation