Energy exchange calculations in a simple mechanical system to investigate the origin of friction

The microscopic origin of friction is an important topic in science and technology. To date, noteworthy aspects of it remain unsolved. In an effort to shed some light on the possible mechanisms that could give rise to the macroscopic emergence of friction, a very simple 1D system of two particles is considered, one of them is free but moving with an initial velocity, and the other confined by a harmonic potential. The two particles interact via a repulsive Gaussian potential. While it represents in a straightforward manner a tip substrate system in the real world, no analytic solutions can be found for its motion. Because of the interaction, the free particle (tip) may overcome the bound particle (substrate) losing part of its kinetic energy. We solve Newton’s equations of the two particles numerically and calculate the net exchange of energy in the asymptotic state in terms of the relevant parameters of the problem. The effective dissipation that emerges from this simple, classical model with no ad hoc terms shows, surprisingly, a range of rich, nontrivial, behavior. We give theoretical reasoning which provides a satisfactory qualitative description. The essential ingredient of that reasoning is that the transfer of energy from the incoming particle to the confined one can be regarded as the source of the emergent dissipation force the friction experienced by the incoming particle.