Remarks on periodic Jacobi matrices on trees
(2021) In Journal of Mathematical Physics 62(4).- 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.
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https://lup.lub.lu.se/record/c5f9f8e9-afb2-4579-8258-41b61b69af39
- author
- Christiansen, Jacob S. LU ; Simon, Barry and Zinchenko, Maxim
- organization
- publishing date
- 2021
- type
- Contribution to journal
- publication status
- published
- subject
- in
- Journal of Mathematical Physics
- volume
- 62
- issue
- 4
- article number
- 042101
- publisher
- American Institute of Physics (AIP)
- external identifiers
-
- scopus:85104102219
- ISSN
- 0022-2488
- DOI
- 10.1063/5.0033702
- language
- English
- LU publication?
- yes
- id
- c5f9f8e9-afb2-4579-8258-41b61b69af39
- date added to LUP
- 2021-04-26 10:36:26
- date last changed
- 2025-04-04 14:25:17
@article{c5f9f8e9-afb2-4579-8258-41b61b69af39,
abstract = {{<p>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. </p>}},
author = {{Christiansen, Jacob S. and Simon, Barry and Zinchenko, Maxim}},
issn = {{0022-2488}},
language = {{eng}},
number = {{4}},
publisher = {{American Institute of Physics (AIP)}},
series = {{Journal of Mathematical Physics}},
title = {{Remarks on periodic Jacobi matrices on trees}},
url = {{http://dx.doi.org/10.1063/5.0033702}},
doi = {{10.1063/5.0033702}},
volume = {{62}},
year = {{2021}},
}