Application of the non-equilibrium statisticaloperator method (NESOM) to dissipation atomic force microscopy

Abstract

We apply the non-equilibrium statistical operator method tonon-contact atomic force microscopy, considering explicitlythe statistical effects of (classical) vibrations of surface atomsand associated energy transfer from the tip to the surface. Wederive several, physically and mathematically equivalent, forms ofthe equation of motion for the tip, each containing a friction termdue to the so-called intrinsic mechanism of energy dissipationfirst suggested by Gauthier and Tsukada. Our exact treatmentsupports the results of some earlier work which were allapproximate. We also demonstrate, using the same theory, that thedistribution function of the tip in the coordinate-momentum phasesubspace is governed by the Fokker-Planck equation and should beconsidered as strongly peaked around the exact values ⟨P⟩t and ⟨Q⟩t of the momentum and theposition of the tip, respectively.