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Crystallization in a One-Dimensional Periodic Landscape

Abstract

We consider the crystallization problem for a finite one-dimensional collection of identical hard spheres in a periodic energy landscape. This issue arises in connection with the investigation of crystalline states of ionic dimers, as well as in epitaxial growth on a crystalline substrate in presence of lattice mismatch. Depending on the commensurability of the radius of the sphere and the period of the landscape, we discuss the possible emergence of crystallized states. In particular, we prove that crystallization in arbitrarily long chains is generically not to be expected.

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Acknowledgements

MF is supported by the DFG-FWF Project FR 4083/3-1/I 4354, and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics–Geometry–Structure. US is partially supported by the Austrian Science Fund (FWF) Project F 65 and by the Vienna Science and Technology Fund (WWTF) Project MA14-009.

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Correspondence to Ulisse Stefanelli.

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Communicated by Alessandro Giuliani.

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Friedrich, M., Stefanelli, U. Crystallization in a One-Dimensional Periodic Landscape. J Stat Phys 179, 485–501 (2020). https://doi.org/10.1007/s10955-020-02537-9

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  • DOI: https://doi.org/10.1007/s10955-020-02537-9

Keywords

  • Crystallization
  • Hard spheres
  • Periodic landscape
  • Ionic dimers
  • Epitaxial growth

Mathematics Subject Classification

  • 82D25