Journal of Statistical Physics

, Volume 47, Issue 3, pp 409-438

First online:

One-dimensional model of the quasicrystalline alloy

  • S. E. BurkovAffiliated withLandau Institute for Theoretical Physics

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A one-dimensional chain of atoms of two types is investigated. It is proven exactly for the model of attracting hard spheres that if the ratio of the numbers of atoms of the two types is irrational, then the state of absolutely minimal energy is quasicrystalline. The quasicrystalline state is also investigated in the case of the Lennard-Jones interatomic potential. All the microscopic values (interatomic spacing, electronic density, etc.) are shown to be quasiperiodic functions varying on Cantor sets. Diffraction patterns, electronic properties, and vibrational spectra are also discussed.

Key words

Quasicrystals incommensurability localization groundstate