Nonequilibrium statistical mechanics of mixed quantum classical ensembles: application to noncontact atomic force microscopy.
Using the nonequilibrium statistical operator method, we suggest a new general method of treating dynamics of a combined system consisting of interacting classical and quantum parts. The method is illustrated on the tip dynamics in the noncontact atomic force microscopy (NC-AFM) where a macroscopic tip interacts with a quantum microscopic system (the surface and the nanotip). The derived general equation of motion for the tip and the Fokker-Planck equation, applicable even at low temperatures, contain memory effects and a friction term which should (at least partially) be responsible for the observed energy dissipation in NC-AFM experiments.
Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom.
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Kantorovich