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An exactly solvable model of a multidimensional incommensurate structure

Research paper by A. L. Figotin, L. A. Pastur

Indexed on: 01 Dec '84Published on: 01 Dec '84Published in: Communications in Mathematical Physics



Abstract

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 incommensurability, the spectrum does not contain the absolutely continuous component, while for small incommensurability the spectrum is singular continuous.