Effective discommensurations in the incommensurate ground states of the extended Frenkel-Kontorowa models. (English) Zbl 0716.34050
A multidimensional Frenkel-Kontorowa (FK) model is considered. Provided that the attached phonon spectrum has a nonzero gap, the authors prove that the hull function of an incommensurate ground state is purely discrete. The starting point is the well-known fact that for the 1- dimensional FK model the ground states are of two kinds: commensurate ones (periodic cycles) and incommensurate ones (KAM 1-tori). It follows readily from the result in the paper, that the Fourier coefficients of the incommensurate modulation are given by an analytic hull function.
Reviewer: S.I.Andersson
MSC:
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 37A30 | Ergodic theorems, spectral theory, Markov operators |
References:
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