Effective numerical method of spectral analysis of quantum graphs

被引：7

作者：

Barrera-Figueroa, Victor ^{[1
]}

Rabinovich, Vladimir S. ^{[2
]}

机构：

[1] Inst Politecn Nacl, Posgrad Tecnol Avanzada, SEPI UPIITA, Av Inst Politecn Nal 2580, Mexico City 07340, DF, Mexico

[2] Inst Politecn Nacl, SEPI ESIME, Dept Telecomunicac, Av Inst Politecn Nal S-N, Mexico City 07738, DF, Mexico

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL | 2017年 / 50卷 / 21期

关键词：

periodic quantum graphs; band-gap spectrum; spectral parameter; power series (SPPS); dispersion equation; Dirac points; PARAMETER POWER-SERIES; KIRCHHOFFS RULE; OPERATORS; ZEROS; DISPERSION; MECHANICS; ELECTRONS; EQUATION;

D O I：

10.1088/1751-8121/aa6cc6

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrodinger operators with real-valued periodic electric potentials as Hamiltonians and with Kirchhoff and Neumann conditions at the vertices. Our method is based on the spectral parameter power series method, which leads to a series representation of the dispersion equation, which is suitable for both analytical and numerical calculations. Several important examples demonstrate the effectiveness of our method for some periodic graphs of interest that possess potentials usually found in quantum mechanics.

引用

页数：33