Approximating Spectral invariants of Harper operators on graphs
We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action...
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ftdatacite:10.48550/arxiv.math/0006138 2023-05-15T16:01:31+02:00 Approximating Spectral invariants of Harper operators on graphs Mathai, V. Yates, S. 2000 https://dx.doi.org/10.48550/arxiv.math/0006138 https://arxiv.org/abs/math/0006138 unknown arXiv Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ Functional Analysis math.FA High Energy Physics - Theory hep-th FOS Mathematics FOS Physical sciences 58J22, 46L85, 39A12 Primary 46L60 Secondary article-journal Article ScholarlyArticle Text 2000 ftdatacite https://doi.org/10.48550/arxiv.math/0006138 2022-04-01T16:56:37Z We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action of an amenable discrete group, can be approximated by the average spectral density function of the DMLs on a regular exhaustion, with either Dirichlet or Neumann boundary conditions. This then gives a criterion for the existence of gaps in the spectrum of the DML, as well as other interesting spectral properties of such DMLs. The technique used incorporates some results of algebraic number theory. : 20 pages, Latex2e, final version Text DML DataCite Metadata Store (German National Library of Science and Technology) Harper ENVELOPE(-57.050,-57.050,-84.050,-84.050) |
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DataCite Metadata Store (German National Library of Science and Technology) |
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ftdatacite |
language |
unknown |
topic |
Functional Analysis math.FA High Energy Physics - Theory hep-th FOS Mathematics FOS Physical sciences 58J22, 46L85, 39A12 Primary 46L60 Secondary |
spellingShingle |
Functional Analysis math.FA High Energy Physics - Theory hep-th FOS Mathematics FOS Physical sciences 58J22, 46L85, 39A12 Primary 46L60 Secondary Mathai, V. Yates, S. Approximating Spectral invariants of Harper operators on graphs |
topic_facet |
Functional Analysis math.FA High Energy Physics - Theory hep-th FOS Mathematics FOS Physical sciences 58J22, 46L85, 39A12 Primary 46L60 Secondary |
description |
We study Harper operators and the closely related discrete magnetic Laplacians (DML) on a graph with a free action of a discrete group, as defined by Sunada. A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs with a free action of an amenable discrete group, can be approximated by the average spectral density function of the DMLs on a regular exhaustion, with either Dirichlet or Neumann boundary conditions. This then gives a criterion for the existence of gaps in the spectrum of the DML, as well as other interesting spectral properties of such DMLs. The technique used incorporates some results of algebraic number theory. : 20 pages, Latex2e, final version |
format |
Text |
author |
Mathai, V. Yates, S. |
author_facet |
Mathai, V. Yates, S. |
author_sort |
Mathai, V. |
title |
Approximating Spectral invariants of Harper operators on graphs |
title_short |
Approximating Spectral invariants of Harper operators on graphs |
title_full |
Approximating Spectral invariants of Harper operators on graphs |
title_fullStr |
Approximating Spectral invariants of Harper operators on graphs |
title_full_unstemmed |
Approximating Spectral invariants of Harper operators on graphs |
title_sort |
approximating spectral invariants of harper operators on graphs |
publisher |
arXiv |
publishDate |
2000 |
url |
https://dx.doi.org/10.48550/arxiv.math/0006138 https://arxiv.org/abs/math/0006138 |
long_lat |
ENVELOPE(-57.050,-57.050,-84.050,-84.050) |
geographic |
Harper |
geographic_facet |
Harper |
genre |
DML |
genre_facet |
DML |
op_rights |
Assumed arXiv.org perpetual, non-exclusive license to distribute this article for submissions made before January 2004 http://arxiv.org/licenses/assumed-1991-2003/ |
op_doi |
https://doi.org/10.48550/arxiv.math/0006138 |
_version_ |
1766397341817896960 |