Communications in Mathematical Physics

, Volume 265, Issue 1, pp 165–188 | Cite as

Minimal Configurations for the Frenkel-Kontorova Model on a Quasicrystal

  • Jean-Marc GambaudoEmail author
  • Pierre Guiraud
  • Samuel Petite


In this paper, we consider the Frenkel-Kontorova model of a one dimensional chain of atoms submitted to a potential. This potential splits into an interaction potential and a potential induced by an underlying substrate which is a quasicrystal. Under standard hypotheses, we show that every minimal configuration has a rotation number, that the rotation number varies continuously with the minimal configuration, and that every non negative real number is the rotation number of a minimal configuration. This generalizes well known results obtained by S. Aubry and P.Y. le Daeron in the case of a crystalline substrate.


Neural Network Statistical Physic Real Number Complex System Nonlinear Dynamics 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Jean-Marc Gambaudo
    • 1
    Email author
  • Pierre Guiraud
    • 2
  • Samuel Petite
    • 3
  1. 1.Centro de Modelamiento Matemático, U.M.I. CNRS 2807Universidad de ChileSantiagoChile
  2. 2.Departamento de Ingeniería Matemática, Fac. Ciencias Físicas y MatemáticasUniversidad de ChileSantiagoChile
  3. 3.Institut de Mathématiques de Bourgogne, U.M.R. CNRS 5584Université de Bourgogne, U.F.R. des Sciences et TéchniquesDijon CedexFrance

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