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A model for a driven Frenkel-Kontorova chain
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We study a Frenkel{Kontorova (FK) model of a nite chain with free-end boundary conditions. The model has two competing potentials. Newton trajectories are an ideal tool to understand the circumstances under a driving of an FK chain by external forces. To reach the insights we calculate some stationary structures for a chain with 23 particles. We search the lowest energy saddle points for a complete minimum energy path of the chain for a movement over the full period of the on-site potential, a sliding. If an additional tilting is set, then one is interested in barrier breakdown points (BBPs) on the potential energy surface for a critical tilting force named the static frictional force. In symmetric cases, such BBPs are often valley-ridge in ection points of the potential energy surface. We explain the theory and demonstrate it with an example. We propose a model for a DC drive, as well as an AC drive, of the chain using special directional vectors of the external force.
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QUAPP, Wolfgang and BOFILL I VILLÀ, Josep M. A model for a driven Frenkel-Kontorova chain. European Physical Journal B. 2019. Vol. 92, num. 95. ISSN 1434-6028. [consulted: 22 of May of 2026]. Available at: https://hdl.handle.net/2445/152810