Tomlinson model improved with no ad-hoc dissipation

The origin of friction force is a very old problem in physics, which goes back to Leonardo da Vinci or even older times. Extremely important from a practical point of view, but with no satisfactory explanation yet. Many models have been used to study dry sliding friction. The model introduced in the present work consists in one atom that slide over a surface represented by a periodic arrangement of atoms, each confined by an independent harmonic potential. The novelty of our contribution resides in that we do not include an {\em ad hoc} dissipation term as all previous works have done. Despite the apparent simplicity of the model it can not be solved analytically, so the study is performed solving the Newton's equations numerically. The results obtained so far with the present model are in accordance with the Tomlinson model, often used to represent the atomic force microscope. The atomic-scale analysis of the interaction between sliding surfaces is necessary to understand the non-conservative lateral forces and the mechanism of energy dissipation which can be thought as effective emerging friction.