|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'506'133
Articles rated: 2609
26 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Arithmetic properties of eigenvalues of generalized Harper operators on graphs | | J. Dodziuk
; V. Mathai
; S. Yates
; | | Date: |
18 Nov 2003 | | Subject: | Spectral Theory; Mathematical Physics | math.SP math-ph math.MP | | Abstract: | Let $Qbar$ denote the field of complex algebraic numbers. A discrete group $G$ is said to have the $sigma$-multiplier algebraic eigenvalue property, if for every matrix $A$ with entries in the twisted group ring over the complex algebraic numbers $M_d(Qbar(G,sigma))$, regarded as an operator on $l^2(G)^d$, the eigenvalues of $A$ are algebraic numbers, where $sigma$ is an algebraic multiplier. Such operators include the Harper operator and the discrete magnetic Laplacian that occur in solid state physics. We prove that any finitely generated amenable, free or surface group has this property for any algebraic multiplier $sigma$. In the special case when $sigma$ is rational ($sigma^n$=1 for some positive integer $n$) this property holds for a larger class of groups, containing free groups and amenable groups, and closed under taking directed unions and extensions with amenable quotients. Included in the paper are proofs of other spectral properties of such operators. | | Source: | arXiv, math.SP/0311315 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER