Recently there is a lot of interest in the study of Sturm-Liouville problems on graphs,
called quantum graphs. However the study on cyclic quantum graphs are scarce. In
this thesis, we shall rst consider a characteristic function approach to the spectral
analysis for the Schrodinger operator H acting on graphene-like graphs|in nite periodic
hexagonal graphs with 3 distinct adjacent edges and 3 distinct potentials de ned
on them. We apply the Floquet-Bloch theory to derive a Floquet equation with parameters
theta_1, theta_2, whose roots de ne all the spectral values of H. Then we show that the
spectrum of this operator is continuous. Our results generalize those of Kuchment-Post
and Korotyaev-Lobanov. Our method is also simpler and more direct.
Next we solve two Ambarzumyan problems, one for graphene and another for a cyclic
graph with two vertices and 3 edges. Finally we solve an Hochstadt-Lieberman type
inverse spectral problem for the same cyclic graph with two vertices and 3 edges.
Keywords : quantum graphs, graphene, spectrum, Ambarzumyan problem, inverse
spectral problem.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0730112-120420 |
| Date | 30 July 2012 |
| Creators | Wang, Tui-En |
| Contributors | Tzon-Tzer Lu, Yung-Sze Choi, Chung-Chuan Chen, Chao-Nien Chen, Chung-Tsun Shieh, Chun-Kong Law |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0730112-120420 |
| Rights | user_define, Copyright information available at source archive |
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