An exactly solvable model of a multidimensional incommensurate structure
The paper considers the class of Schrödinger multidimensional discrete operators with quasi-periodic unbounded potential for which essentially complete spectral analysis may be carried out. In the case of sufficiently high incommensurability of almost-periods, the spectrum of such operators is found to be pure point and simple, the eigenfunctions exponentially localized and the low frequency conductivity exponentially small. In the one-dimensional case, for any incommemsurability, the spectrum does not contain the absolutely continuous component, while for small incommensurability the spectrum is singular continuous.
Schrödinger multidimensional discrete operators
scientific article; zbMATH DE number 3931605