An exactly solvable model of a multidimensional incommensurate structure
type: Item
instance of: scholarly article
title: An exactly solvable model of a multidimensional incommensurate structure
zbMATH Open document ID: 0582.35101
DOI: 10.1007/BF01210831
author: A. Figotin
author: L. A. Pastur
published in: Communications in Mathematical Physics
publication date: 1984-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 35J10
Mathematics Subject Classification ID: 35P05
zbMATH DE Number: 3931605
zbMATH Keywords: Schrödinger multidimensional discrete operators
zbMATH Keywords: quasi-periodic unbounded potential
zbMATH Keywords: spectrum
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01210831
OpenAlex ID: W1997899880
description: scientific article; zbMATH DE number 3931605