On the Spectra of Carbon Nano-Structures

被引:0
作者
Peter Kuchment
Olaf Post
机构
[1] Texas A&M University,Mathematics Department
[2] Humboldt-Universität zu Berlin,Institut für Mathematik
来源
Communications in Mathematical Physics | 2007年 / 275卷
关键词
Dispersion Relation; Conical Singularity; Monodromy Matrix; Simple Loop; Quantum Graph;
D O I
暂无
中图分类号
学科分类号
摘要
An explicit derivation of dispersion relations and spectra for periodic Schrödinger operators on carbon nano-structures (including graphene and all types of single-wall nano-tubes) is provided.
引用
收藏
页码:805 / 826
页数:21
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[21]  
Trubowitz E.(2005)Quantum graphs. II. Some spectral properties of quantum and combinatorial graphs J. Phys. A 38 4887-4900
[22]  
Garnett J.(1999)Spectral Properties of High Contrast Band-Gap Materials and Operators on Graphs Exp. Math. 8 1-28
[23]  
Trubowitz E.(2001)Integral representations and Liouville theorems for solutions of periodic elliptic equations J. Funct. Anal. 181 402-446
[24]  
Gerard C.(2006)On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators Commun. Math. Phys. 268 673-686
[25]  
Nier F.(1974)Asymptotics of the width of gaps in the spectrum of the Sturm-Liouville operators with periodic potential Soviet Math. Dokl. 15 649-653
[26]  
Hochstadt H.(1975)A characterization of the spectrum of Hill’s operator Matem. Sborn. 97 540-606
[27]  
Hochstadt H.(1978)Hill’s surfaces and their theta functions Bull. Amer. Math. Soc. 84 1042-1085
[28]  
Katsnelson M.I.(1970)Quantum theory on a network. II. A solvable model which may have several bound states per node point J. Math. Phys. 11 2525-2538
[29]  
Kostrykin V.(1970)Quantum theory on a network. I. A solvable model whose wavefunctions are elementary functions J. Math. Phys. 11 635-648
[30]  
Schrader R.(2004)Analysis of the dispersion equation for the Schrödinger operator on periodic metric graphs Waves in Random Media 14 157-183