Measure zero spectrum of a class of Schrödinger operators

Qing Hui Liu; Bo Tan; Zhi Xiong Wen; Jun Wu

doi:10.1023/A:1013718624572

Measure zero spectrum of a class of Schrödinger operators

Qing Hui Liu^*, Bo Tan, Zhi Xiong Wen, Jun Wu

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

26 Citations (Scopus)

Abstract

We study the measure of the spectrum of a class of one-dimensional discrete Schrödinger operators H_ν,ω with potential ν(ω) generated by any primitive substitutions. It is well known that the spectrum of H_ν,ω is singular continuous. We will give a more exact result that the spectrum of H_ν,ω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.

Original language	English
Pages (from-to)	681-691
Number of pages	11
Journal	Journal of Statistical Physics
Volume	106
Issue number	3-4
DOIs	https://doi.org/10.1023/A:1013718624572
Publication status	Published - 2002
Externally published	Yes

Keywords

Primitive substitution
Schrödinger operator
Spectrum
Trace map

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10.1023/A:1013718624572

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Liu, Q. H., Tan, B., Wen, Z. X., & Wu, J. (2002). Measure zero spectrum of a class of Schrödinger operators. Journal of Statistical Physics, 106(3-4), 681-691. https://doi.org/10.1023/A:1013718624572

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abstract = "We study the measure of the spectrum of a class of one-dimensional discrete Schr{\"o}dinger operators Hν,ω with potential ν(ω) generated by any primitive substitutions. It is well known that the spectrum of Hν,ω is singular continuous. We will give a more exact result that the spectrum of Hν,ω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.",

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author = "Liu, {Qing Hui} and Bo Tan and Wen, {Zhi Xiong} and Jun Wu",

year = "2002",

doi = "10.1023/A:1013718624572",

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volume = "106",

pages = "681--691",

journal = "Journal of Statistical Physics",

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T1 - Measure zero spectrum of a class of Schrödinger operators

AU - Liu, Qing Hui

AU - Tan, Bo

AU - Wen, Zhi Xiong

AU - Wu, Jun

PY - 2002

Y1 - 2002

N2 - We study the measure of the spectrum of a class of one-dimensional discrete Schrödinger operators Hν,ω with potential ν(ω) generated by any primitive substitutions. It is well known that the spectrum of Hν,ω is singular continuous. We will give a more exact result that the spectrum of Hν,ω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.

AB - We study the measure of the spectrum of a class of one-dimensional discrete Schrödinger operators Hν,ω with potential ν(ω) generated by any primitive substitutions. It is well known that the spectrum of Hν,ω is singular continuous. We will give a more exact result that the spectrum of Hν,ω is a set of Lebesgue measure zero, by removing two hypotheses (the semi-primitive of a certain induced substitution and the existence of square word) from a theorem due to Bovier and Ghez.

KW - Primitive substitution

KW - Schrödinger operator

KW - Spectrum

KW - Trace map

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U2 - 10.1023/A:1013718624572

DO - 10.1023/A:1013718624572

M3 - Article

AN - SCOPUS:0036103188

SN - 0022-4715

VL - 106

SP - 681

EP - 691

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 3-4

ER -

Measure zero spectrum of a class of Schrödinger operators

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Keywords

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