An elementary introduction to quantum graphs

被引：39
作者：
Berkolaiko, Gregory [1 ]
机构：
[1] Texas A&M Univ, Dept Math, College Stn, TX 77843 USA
来源：
GEOMETRIC AND COMPUTATIONAL SPECTRAL THEORY | 2017年 / 700卷
关键词：
WEYL RESONANCE ASYMPTOTICS; NODAL COUNT; SCATTERING; EIGENVALUE; DOMAINS; CHAOS;
D O I：
10.1090/conm/700/14182
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We describe some basic tools in the spectral theory of Schrodinger operator on metric graphs (also known as "quantum graphs") by studying in detail some basic examples. The exposition is kept as elementary and accessible as possible. In the later sections we apply these tools to prove some results on the count of zeros of the eigenfunctions of quantum graphs.
引用
收藏
页码：41 / 72
页数：32
相关论文
共 51 条
[1]  
[Anonymous], 2013, Matrix Analysis
[2]  
Ariturk S, 2016, ARXIV160907471
[3]   Finite pseudo orbit expansions for spectral quantities of quantum graphs [J].
Band, R. ;
Harrison, J. M. ;
Joyner, C. H. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2012, 45 (32)
[4]  
Band R, 2016, ARXIV160800520
[5]  
Band R., 2016, SYMMETRY QUANT UNPUB
[6]  
Band R, 2008, P SYMP PURE MATH, V77, P5
[7]   Nodal domains on isospectral quantum graphs: the resolution of isospectrality? [J].
Band, Ram ;
Shapira, Talia ;
Smilansky, Uzy .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2006, 39 (45) :13999-14014
[8]   Anomalous nodal count and singularities in the dispersion relation of honeycomb graphs [J].
Band, Ram ;
Berkolaiko, Gregory ;
Weyand, Tracy .
JOURNAL OF MATHEMATICAL PHYSICS, 2015, 56 (12)
[9]   Universality of the Momentum Band Density of Periodic Networks [J].
Band, Ram ;
Berkolaiko, Gregory .
PHYSICAL REVIEW LETTERS, 2013, 111 (13)
[10]   Dynamics of Nodal Points and the Nodal Count on a Family of Quantum Graphs [J].
Band, Ram ;
Berkolaiko, Gregory ;
Smilansky, Uzy .
ANNALES HENRI POINCARE, 2012, 13 (01) :145-184
123456