Asymptotics of the Eigenvalues and Eigenfunctions of a Thin Square Dirichlet Lattice with a Curved Ligament

S. A. Nazarov

Результат исследований: Научные публикации в периодических изданияхстатья

Выдержка

The spectrum of the Dirichlet problem on the planar square lattice of thin quantum waveguides has a band-gap structure with short spectral bands separated by wide spectral gaps. The curving of at least one of the ligaments of the lattice generates points of the discrete spectrum inside gaps. A complete asymptotic series for the eigenvalues and eigenfunctions are constructed and justified; those for the eigenfunctions exhibit a remarkable behavior imitating the rapid decay of the trapped modes: the terms of the series have compact supports that expand unboundedly as the number of the term increases.

Язык оригиналаанглийский
Страницы (с-по)559-579
ЖурналMathematical Notes
Том105
Номер выпуска3-4
DOI
СостояниеОпубликовано - 1 мар 2019

Отпечаток

Eigenvalues and Eigenfunctions
Dirichlet
Asymptotic series
Spectral Gap
Lattice Points
Discrete Spectrum
Compact Support
Band Gap
Term
Square Lattice
Dirichlet Problem
Expand
Waveguide
Eigenfunctions
Decay
Series

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Asymptotics of the Eigenvalues and Eigenfunctions of a Thin Square Dirichlet Lattice with a Curved Ligament. / Nazarov, S. A.

В: Mathematical Notes, Том 105, № 3-4, 01.03.2019, стр. 559-579.

Результат исследований: Научные публикации в периодических изданияхстатья

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