Spectrum of 1D quasicrystals near the periodic chain
Résumé
A tight binding model on the general 1D quasiperiodic chain is studied in the framework of perturbation theory, near the corresponding periodic chain, using a new set of coordinates. The main gaps are well described, whereas the very small ones are correctly given, only for a very small perturbation. For a given irrational number, the energies where the gaps appear in the periodic chain spectrum, are exactly derived.