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Remarks on periodic Jacobi matrices on trees

Christiansen, Jacob S. LU ; Simon, Barry and Zinchenko, Maxim (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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author
; and
organization
publishing date
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
2021-04-26 10:36:26
@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},
}