\(\mathcal{RT}\)-symmetric Laplace operators on star graphs: real spectrum and self-adjointness
type: Item
instance of: scholarly article
title: \(\mathcal{RT}\)-symmetric Laplace operators on star graphs: real spectrum and self-adjointness
zbMATH Open document ID: 1337.81062
DOI: 10.1155/2015/649795
author: Maria Astudillo
author: Pavel Kurasov
author: Muhammad Usman
published in: Advances in Mathematical Physics
publication date: 2016-05-02T00:00:00Z
review text: Summary: How ideas of \(\mathcal{PT}\)-symmetric quantum mechanics can be applied to quantum graphs is analyzed, in particular to the star graph. The class of rotationally symmetric vertex conditions is analyzed. It is shown that all such conditions can effectively be described by circulant matrices: real in the case of odd number of edges and complex having particular block structure in the even case. Spectral properties of the corresponding operators are discussed.
Mathematics Subject Classification ID: 81Q35
Mathematics Subject Classification ID: 81R05
Mathematics Subject Classification ID: 81Q10
Mathematics Subject Classification ID: 35J05
zbMATH DE Number: 6575802
Wikidata QID: Q59102528
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/649795
OpenAlex ID: W1743149844
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description: scientific article; zbMATH DE number 6575802