Quantum stick-slip motion in nanoscaled friction

Friction in atomistic systems is usually described by the classical Prandtl-Tomlinson model suitable for capturing the dragging force of a nanoparticle in a periodic potential. Here we consider the quantum mechanical version of this model in which the dissipation is facilitated by releasing heat to an external bath reservoir. The time evolution of the system is captured with the Liouville-von Neumann equation through the density matrix of the system in the Markov approximation. We examine several kinetic and dissipative properties of the nanoparticle by delineating classical vs quantum mechanical effects. We find that the Landau-Zener tunneling is a key factor in the overall reduction of the frictional dissipation when compared to the classical motion in which such tunneling is absent. Other regimes of motion, controlled by the corrugation parameter and other properties, are also found. This in-depth study analyzes the interplay between velocity, strength of interaction, and temperature to control the frictional force and provide useful guidelines for experimental data interpretation.