Quantum friction for a scalar model: spatial dependence and higher orders

We use a perturbative approach to evaluate transition amplitudes corresponding to quantum friction, for a scalar model describing an atom which moves at a constant velocity, close to a material plane. In particular, we present results on the probability density per unit time of exciting degrees of freedom on specific regions of the plane. This allows one to know spatial features of the effect which could have practical relevance, for instance, for the design of nanodevices.