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We consider a linear Boltzmann equation that arises in a model for quantumfriction. It describes a particle that is slowed down by the emission ofbosons. We study the stochastic process generated by this Boltzmann equationand we show convergence of its spatial trajectory to a multiple of Brownianmotion with exponential scaling. The asymptotic position of the particle isfinite in mean, even though its absolute value is typically infinite. This iscontrasted to an approximation that neglects the influence of fluctuations,where the mean asymptotic position is infinite.

Fluctuations in a kinetic transport model for quantum friction