Minimal Configurations for the Frenkel-kontorova Model on a Quasicrystal by Jean-marc Gambaudo, Pierre Guiraud and Samuel Petite
نویسندگان
چکیده
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. Date: February 7, 2008. 1 2 J.-M. Gambaudo, P. Guiraud and S. Petite
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