Minimal Configurations for the Frenkel-Kontorova Model on a Quasicrystal
| Autor: | J-M. Gambaudo, S. Petite, P. Guiraud |
|---|---|
| Přispěvatelé: | Center for Mathematical Modelling - Centro de Modelamiento Matematico [Santiago] (CMM), Universidad de Chile = University of Chile [Santiago] (UCHILE)-Centre National de la Recherche Scientifique (CNRS), Departamento de Ingenería Matemática, (Departamento de Ingenería Matemática,), Institut de Mathématiques de Bourgogne [Dijon] (IMB), Centre National de la Recherche Scientifique (CNRS)-Université de Franche-Comté (UFC), Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université Bourgogne Franche-Comté [COMUE] (UBFC)-Université de Bourgogne (UB) |
| Rok vydání: | 2006 |
| Předmět: |
Physics
Frenkel–Kontorova model [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 010102 general mathematics Mathematical analysis FOS: Physical sciences Quasicrystal Statistical and Nonlinear Physics Mathematical Physics (math-ph) Dynamical Systems (math.DS) 01 natural sciences 010101 applied mathematics Interaction potential Chain (algebraic topology) FOS: Mathematics 37N20 52C23 82B20 Mathematics - Dynamical Systems 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematical Physics Rotation number Real number |
| Zdroj: | Communications in Mathematical Physics Communications in Mathematical Physics, Springer Verlag, 2006, 265 (1), pp.165-188. ⟨10.1007/s00220-006-1531-x⟩ |
| ISSN: | 1432-0916 0010-3616 |
| DOI: | 10.1007/s00220-006-1531-x |
| Popis: | 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. Comment: 25 pages, 8 figures |
| Databáze: | OpenAIRE |
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