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Remarks on periodic Jacobi matrices on trees

Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim (2021) Remarks on periodic Jacobi matrices on trees. Journal of Mathematical Physics, 62 (4). Art. No. 042101. ISSN 0022-2488. doi:10.1063/5.0033702. https://resolver.caltech.edu/CaltechAUTHORS:20210423-080608586

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Abstract

We look at periodic Jacobi matrices on trees. We provide upper and lower bounds on the gap of such operators analogous to the well-known gap in the spectrum of the Laplacian on the upper half-plane with a hyperbolic metric. We make some conjectures about antibound states and make an interesting observation for the so-called rg-model where the underlying graph has r red and g green vertices and where any two vertices of different colors are connected by a single edge.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1063/5.0033702DOIArticle
https://arxiv.org/abs/2010.01701arXivDiscussion Paper
ORCID:
AuthorORCID
Christiansen, Jacob S.0000-0002-3417-8574
Simon, Barry0000-0003-2561-8539
Zinchenko, Maxim0000-0002-9559-0650
Additional Information:© 2021 Published under license by AIP Publishing. Submitted: 18 October 2020; Accepted: 19 March 2021; Published Online: 13 April 2021. J.S.C. and M.Z. would like to thank F. Harrison and E. Mantovan for the hospitality of Caltech where some of this work was done. This work was partially supported by the Swedish Research Council (VR) under Grant No. 2018-03500 (J.S.C.), the NSF grant, No. DMS-1665526 (B.S.), and the Simons Foundation grant, No. CGM-581256 (M.Z.). Data Availability: Data sharing is not applicable to this article as no new data were created or analyzed in this study.
Funders:
Funding AgencyGrant Number
Swedish Research Council2018-03500
NSFDMS-1665526
Simons FoundationCGM-581256
Issue or Number:4
DOI:10.1063/5.0033702
Record Number:CaltechAUTHORS:20210423-080608586
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20210423-080608586
Official Citation:Remarks on periodic Jacobi matrices on trees. J. Math. Phys. 62, 042101 (2021); doi: 10.1063/5.0033702
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:108807
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:23 Apr 2021 17:44
Last Modified:23 Apr 2021 17:44

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