A family of almost periodic Schrödinger operators

Goerge A. Baker, D. Bessis and P. Moussa

Physica A: Statistical Mechanics and its Applications, 1984, vol. 124, issue 1, 61-77

Abstract: Bellissard et al.1 introduced a one-dimensional, almost-periodic, discrete Schrödinger operator which is defined by a parameter λ. We allow this parameter to become complex and develop a geometric formalism to control the operator. The support of the spectrum of this operator is the Julia set of the mapping x→x2-λ. We prove that the almost-periodicity holds over wide regions of the complex λ-plane, even though Hermiticity fails.

Date: 1984
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:124:y:1984:i:1:p:61-77

DOI: 10.1016/0378-4371(84)90227-9

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