Quantum and spectral properties of the Labyrinth model. (English) Zbl 1342.82147
Summary: We consider the Labyrinth model, which is a two-dimensional quasicrystal model. We show that the spectrum of this model, which is known to be a product of two Cantor sets, is an interval for small values of the coupling constant. We also consider the density of states measure of the Labyrinth model and show that it is absolutely continuous with respect to Lebesgue measure for almost all values of coupling constants in the small coupling regime.{
©2016 American Institute of Physics}
©2016 American Institute of Physics}
MSC:
| 82D25 | Statistical mechanics of crystals |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 28A80 | Fractals |
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