Approximating spectral invariants of Harper operators on graphs
Abstract. 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 [Sun]. A main result in this paper is that the spectral density function of DMLs associated to rational weight functions on graphs wi...
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ftciteseerx:oai:CiteSeerX.psu:10.1.1.239.7281 2023-05-15T16:01:28+02:00 Approximating spectral invariants of Harper operators on graphs Varghese Mathai Stuart Yates The Pennsylvania State University CiteSeerX Archives application/pdf http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7281 http://arxiv.org/pdf/math/0006138v3.pdf en eng http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7281 http://arxiv.org/pdf/math/0006138v3.pdf Metadata may be used without restrictions as long as the oai identifier remains attached to it. http://arxiv.org/pdf/math/0006138v3.pdf text ftciteseerx 2016-01-07T19:06:19Z Abstract. 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 [Sun]. 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. Text DML Unknown Harper ENVELOPE(-57.050,-57.050,-84.050,-84.050) |
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English |
description |
Abstract. 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 [Sun]. 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. |
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The Pennsylvania State University CiteSeerX Archives |
format |
Text |
author |
Varghese Mathai Stuart Yates |
spellingShingle |
Varghese Mathai Stuart Yates Approximating spectral invariants of Harper operators on graphs |
author_facet |
Varghese Mathai Stuart Yates |
author_sort |
Varghese Mathai |
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 |
url |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7281 http://arxiv.org/pdf/math/0006138v3.pdf |
long_lat |
ENVELOPE(-57.050,-57.050,-84.050,-84.050) |
geographic |
Harper |
geographic_facet |
Harper |
genre |
DML |
genre_facet |
DML |
op_source |
http://arxiv.org/pdf/math/0006138v3.pdf |
op_relation |
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.239.7281 http://arxiv.org/pdf/math/0006138v3.pdf |
op_rights |
Metadata may be used without restrictions as long as the oai identifier remains attached to it. |
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1766397306745126912 |