Research output: Contribution to journal › Article › peer-review
Rectangular lattices of cylindrical quantum waveguides. I. Spectral problems in a finite cross. / Bakharev , F.L.; Matveenko, S.G.; Nazarov, S.A.
In: St. Petersburg Mathematical Journal, Vol. 29, No. 3, 2018, p. 423-437.Research output: Contribution to journal › Article › peer-review
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TY - JOUR
T1 - Rectangular lattices of cylindrical quantum waveguides. I. Spectral problems in a finite cross
AU - Bakharev , F.L.
AU - Matveenko, S.G.
AU - Nazarov, S.A.
PY - 2018
Y1 - 2018
N2 - The spectrum of truncated cross-shaped waveguides is studied under the Dirichlet conditions on the lateral surface and various boundary conditions on the ends of the column and the cross bar. The monotonicity and asymptotics of the eigenvalues are discussed in dependence on the size of a cross whose section may be fairly arbitrary. In the case of a round section, the estimates found for the second eigenvalue agree with the asymptotic formulas obtained. Such information is needed for the spectral analysis of thin periodic lattices of quantum waveguides.
AB - The spectrum of truncated cross-shaped waveguides is studied under the Dirichlet conditions on the lateral surface and various boundary conditions on the ends of the column and the cross bar. The monotonicity and asymptotics of the eigenvalues are discussed in dependence on the size of a cross whose section may be fairly arbitrary. In the case of a round section, the estimates found for the second eigenvalue agree with the asymptotic formulas obtained. Such information is needed for the spectral analysis of thin periodic lattices of quantum waveguides.
UR - https://www.ams.org/journals/spmj/2018-29-03/home.html
M3 - Article
VL - 29
SP - 423
EP - 437
JO - St. Petersburg Mathematical Journal
JF - St. Petersburg Mathematical Journal
SN - 1061-0022
IS - 3
ER -
ID: 35209787