Non-equilibrium dynamics of a classical tip interacting with a quantumsurface

Abstract

We apply the non-equilibrium statistical operator method within themixed quantum–classical representation to the non-contact atomic forcemicroscopy system in which a macroscopic tip is made to oscillate above asample surface. In our treatment the tip is treated classically, whereas amicroscopic system comprising atoms in the surface and in the nano-tip isconsidered quantum mechanically. Using a very general non-Markovianapproach, we obtain both the Fokker–Planck equation for the tip and,independently, its equation of motion with friction terms and memory effectscompletely accounted for. In the classical limit (high temperatures) ourequations turn exactly into the classical counterparts derived previously.