Spatial dependence of quantum friction amplitudes in a scalar model

We study the spatial dependence of the quantum friction effect for an atom moving at a constant velocity, in a parallel direction to a material plane. In particular, we determine the probability per unit time and unit area, for exciting degrees of freedom on the plane, as a function of their position, for a given trajectory of the atom. We also show that the result of integrating out the probability density agrees with previous results for the same system.