TY - JOUR
T1 - Numerical estimates of the essential spectra of quantum graphs with delta-interactions at vertices
AU - Barrera-Figueroa, Víctor
AU - Rabinovich, Vladimir S.
AU - Rosas, Miguel Maldonado
N1 - Publisher Copyright:
© 2017, © 2017 Informa UK Limited, trading as Taylor & Francis Group.
PY - 2019/1/25
Y1 - 2019/1/25
N2 - In this paper, we consider periodic metric graphs embedded in Rn, equipped by Schrödinger operators with bounded potentials q, and δ-type vertex conditions. Graphs are periodic with respect to a group G isomorphic to Zm. Applying the limit operators method, we give a formula for the essential spectra of associated unbounded operators consisting of a union of the spectra of the limit operators defined by the potential q. We apply this formula and the spectral parameter power series (SPPS) method for the analysis of the essential spectral of Schrödinger operators with potentials q of the form q = q0 + q1, where q0 is a periodic potential and q1 is a slowly oscillating at infinity potential. The conjunction of both methods lead to an effective technique that can be used for performing numerical analysis as well. Several numerical examples demonstrate the effectiveness of our approach.
AB - In this paper, we consider periodic metric graphs embedded in Rn, equipped by Schrödinger operators with bounded potentials q, and δ-type vertex conditions. Graphs are periodic with respect to a group G isomorphic to Zm. Applying the limit operators method, we give a formula for the essential spectra of associated unbounded operators consisting of a union of the spectra of the limit operators defined by the potential q. We apply this formula and the spectral parameter power series (SPPS) method for the analysis of the essential spectral of Schrödinger operators with potentials q of the form q = q0 + q1, where q0 is a periodic potential and q1 is a slowly oscillating at infinity potential. The conjunction of both methods lead to an effective technique that can be used for performing numerical analysis as well. Several numerical examples demonstrate the effectiveness of our approach.
KW - 34B45
KW - 34K28
KW - 34L16
KW - 81Q10
KW - 81Q35
KW - 81U30
KW - Periodic quantum graphs
KW - dispersion equation
KW - limit operators method
KW - slowly oscillating at infinity potential
KW - spectral parameter power series (SPPS) method
UR - http://www.scopus.com/inward/record.url?scp=85039551802&partnerID=8YFLogxK
U2 - 10.1080/00036811.2017.1419201
DO - 10.1080/00036811.2017.1419201
M3 - Artículo
SN - 0003-6811
VL - 98
SP - 458
EP - 482
JO - Applicable Analysis
JF - Applicable Analysis
IS - 1-2
ER -