TY - JOUR

T1 - Effective masses for Laplacians on periodic graphs

AU - Korotyaev, E.

AU - Saburova, N.

PY - 2016

Y1 - 2016

N2 - We consider Laplacians on both periodic discrete and periodic metric equilateral graphs. Their spectrum consists of an absolutely continuous part (which is a union of non-degenerate spectral bands) and flat bands, i.e., eigenvalues of infinite multiplicity. We estimate effective masses associated with the ends of each spectral band in terms of geometric parameters of the graphs. Moreover, in the case of the bottom of the spectrum we determine two-sided estimates on the effective mass in terms of geometric parameters of the graphs. The proof is based on Floquet theory, factorization of fiber operators, perturbation theory and the relation between effective masses for Laplacians on discrete and metric graphs obtained in our paper.

AB - We consider Laplacians on both periodic discrete and periodic metric equilateral graphs. Their spectrum consists of an absolutely continuous part (which is a union of non-degenerate spectral bands) and flat bands, i.e., eigenvalues of infinite multiplicity. We estimate effective masses associated with the ends of each spectral band in terms of geometric parameters of the graphs. Moreover, in the case of the bottom of the spectrum we determine two-sided estimates on the effective mass in terms of geometric parameters of the graphs. The proof is based on Floquet theory, factorization of fiber operators, perturbation theory and the relation between effective masses for Laplacians on discrete and metric graphs obtained in our paper.

KW - Effective massesLaplace operatorPeriodic graph

M3 - Article

VL - 436

SP - 104–-130

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - No 1

ER -