Minimal configurations for Frenkel-Kontorova model on a quasicrystal

Details Minimal configurations for Frenkel-Kontorova model on a quasicrystal Minimal configurations for Frenkel-Kontorova model on a quasicrystal

2005-11-03

arxiv.org/abs/math-ph/0511012v1

Physics

Mathematical Physics

25 pages, 8 figures

Scientific paper

10.1007/s00220-006-1531-x

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.

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