An exactly solvable model of a multidimensional incommensurate structure. (English) Zbl 0582.35101

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.


35Q99 Partial differential equations of mathematical physics and other areas of application
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
Full Text: DOI


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