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A model for a driven Frenkel–Kontorova chain

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Abstract

We study a Frenkel–Kontorova (FK) model of a finite 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 inflection 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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Authors and Affiliations

  1. Mathematisches Institut, Universität Leipzig, PF 100920, 04009, Leipzig, Germany

    Wolfgang Quapp

  2. Departament de Química Inorgànica i Orgànica, Secció de Química Orgànica, and Institut de Química Teòrica i Computacional, (IQTCUB), Universitat de Barcelona, Martí i Franquès 1, 08028, Barcelona, Spain

    Josep Maria Bofill

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  1. Wolfgang Quapp
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  2. Josep Maria Bofill
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Correspondence to Wolfgang Quapp.

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Quapp, W., Bofill, J.M. A model for a driven Frenkel–Kontorova chain. Eur. Phys. J. B 92, 95 (2019). https://doi.org/10.1140/epjb/e2019-90703-0

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