Stick-slip statistics in atomic friction

We theoretically study atomic friction experiments in the stick-slip regime within the framework of the Prandtl-Tomlinson model. We derive a differential equation describing the force probability distribution. Approximate analytical solutions of this equation are found for the asymptotic cases of high and low effective spring constant, but for arbitrary pulling velocities. Excellent accuracy of these approximate expressions is demonstrated numerically. In particular, the result for the mean force, although obtained for small spring constants, is shown to be accurate also somewhat outside of its expected validity range.