TY - JOUR
T1 - Effective numerical method of spectral analysis of quantum graphs
AU - Barrera-Figueroa, Víctor
AU - Rabinovich, Vladimir S.
N1 - Publisher Copyright:
© 2017 IOP Publishing Ltd.
PY - 2017/5/4
Y1 - 2017/5/4
N2 - We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger 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.
AB - We present in the paper an effective numerical method for the determination of the spectra of periodic metric graphs equipped by Schrödinger 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.
KW - Dirac points
KW - band-gap spectrum
KW - dispersion equation
KW - periodic quantum graphs
KW - spectral parameter power series (SPPS)
UR - http://www.scopus.com/inward/record.url?scp=85019122471&partnerID=8YFLogxK
U2 - 10.1088/1751-8121/aa6cc6
DO - 10.1088/1751-8121/aa6cc6
M3 - Artículo
SN - 1751-8113
VL - 50
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 21
M1 - 215207
ER -