Calibrated Configurations for Frenkel–Kontorova Type Models in Almost Periodic Environments
| Autor: | Eduardo Garibaldi, Samuel Petite, Philippe Thieullen |
|---|---|
| Přispěvatelé: | Instituto de Matemática, Estatística e Computação Científica [Brésil] (IMECC), Universidade Estadual de Campinas (UNICAMP), Laboratoire Amiénois de Mathématique Fondamentale et Appliquée (LAMFA), Université de Picardie Jules Verne (UPJV)-Centre National de la Recherche Scientifique (CNRS), Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Nuclear and High Energy Physics
Mathematics::Dynamical Systems Kolmogorov–Arnold–Moser theorem [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] 010102 general mathematics Mathematical analysis Statistical and Nonlinear Physics Context (language use) Delone set Type (model theory) Dynamical system 01 natural sciences 010101 applied mathematics Set (abstract data type) Chain (algebraic topology) 0101 mathematics Focus (optics) ComputingMilieux_MISCELLANEOUS Mathematical Physics Mathematics |
| Zdroj: | Annales Henri Poincaré Annales Henri Poincaré, Springer Verlag, 2017, 18 (9), pp.2905-2943. ⟨10.1007/s00023-017-0589-7⟩ |
| ISSN: | 1424-0637 1424-0661 |
| DOI: | 10.1007/s00023-017-0589-7⟩ |
| Popis: | The Frenkel–Kontorova model describes how an infinite chain of atoms minimizes the total energy of the system when the energy takes into account the interaction of nearest neighbors as well as the interaction with an exterior environment. An almost periodic environment leads to consider a family of interaction energies which is stationary with respect to a minimal topological dynamical system. We focus, in this context, on the existence of calibrated configurations (a notion stronger than the standard minimizing condition). In any dimension and for any continuous superlinear interaction energies, we exhibit a set, called projected Mather set, formed of environments that admit calibrated configurations. In the one-dimensional setting, we then give sufficient conditions on the family of interaction energies that guarantee the existence of calibrated configurations for every environment. The main mathematical tools for this study are developed in the frameworks of discrete weak KAM theory, Aubry–Mather theory and spaces of Delone sets. |
| Databáze: | OpenAIRE |
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