Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice

Motoko Kotani

doi:10.1016/S0393-0440(02)00226-7

Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice

Motoko Kotani

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

4 Citations (Scopus)

Abstract

A magnetic transition operator on a crystal lattice is defined as a generalization of the Harper operator. Following the idea of J. Bellissard, we prove Lipschitz continuity of the band edges of its spectrum as magnetic field changes.

Original language	English
Pages (from-to)	323-342
Number of pages	20
Journal	Journal of Geometry and Physics
Volume	47
Issue number	2-3
DOIs	https://doi.org/10.1016/S0393-0440(02)00226-7
Publication status	Published - 2003 Aug

Keywords

Crystal lattice
Group C-algebra
Magnetic transition operator
Weyl representation

ASJC Scopus subject areas

Mathematical Physics
Physics and Astronomy(all)
Geometry and Topology

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10.1016/S0393-0440(02)00226-7

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title = "Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice",

abstract = "A magnetic transition operator on a crystal lattice is defined as a generalization of the Harper operator. Following the idea of J. Bellissard, we prove Lipschitz continuity of the band edges of its spectrum as magnetic field changes.",

keywords = "Crystal lattice, Group C-algebra, Magnetic transition operator, Weyl representation",

author = "Motoko Kotani",

note = "Funding Information: The author would like to express her gratitude to Sunada for useful discussions. She appreciates Bellissard sending their unpublished article [4] , from which she learns much. This work was done during the author{\textquoteright}s stay in I.H.E.S., France. She gratefully acknowledge financial support by the C.N.R.S. and hospitality of the institute. Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.",

year = "2003",

month = aug,

doi = "10.1016/S0393-0440(02)00226-7",

language = "English",

volume = "47",

pages = "323--342",

journal = "Journal of Geometry and Physics",

issn = "0393-0440",

publisher = "Elsevier",

number = "2-3",

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TY - JOUR

T1 - Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice

AU - Kotani, Motoko

N1 - Funding Information: The author would like to express her gratitude to Sunada for useful discussions. She appreciates Bellissard sending their unpublished article [4] , from which she learns much. This work was done during the author’s stay in I.H.E.S., France. She gratefully acknowledge financial support by the C.N.R.S. and hospitality of the institute. Copyright: Copyright 2004 Elsevier Science B.V., Amsterdam. All rights reserved.

PY - 2003/8

Y1 - 2003/8

N2 - A magnetic transition operator on a crystal lattice is defined as a generalization of the Harper operator. Following the idea of J. Bellissard, we prove Lipschitz continuity of the band edges of its spectrum as magnetic field changes.

AB - A magnetic transition operator on a crystal lattice is defined as a generalization of the Harper operator. Following the idea of J. Bellissard, we prove Lipschitz continuity of the band edges of its spectrum as magnetic field changes.

KW - Crystal lattice

KW - Group C-algebra

KW - Magnetic transition operator

KW - Weyl representation

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DO - 10.1016/S0393-0440(02)00226-7

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SP - 323

EP - 342

JO - Journal of Geometry and Physics

JF - Journal of Geometry and Physics

SN - 0393-0440

IS - 2-3

ER -

Lipschitz continuity of the spectra of the magnetic transition operators on a crystal lattice

Abstract

Keywords

ASJC Scopus subject areas

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