R. R. Gadyl'shin, “Local Perturbations of Quantum Waveguides”, TMF, 145:3 (2005), 358–371; Theoret. and Math. Phys., 145:3 (2005), 1678

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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 145, Number 3, Pages 358–371
DOI: https://doi.org/10.4213/tmf1905 (Mi tmf1905)

This article is cited in 34 scientific papers (total in 34 papers)

Local Perturbations of Quantum Waveguides

R. R. Gadyl'shin

Bashkir State Pedagogical University

Full-text PDF (259 kB) Citations (34)

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DOI: https://doi.org/10.4213/tmf1905

Abstract: We give necessary and sufficient conditions for the occurrence of eigenvalues of the Schrodinger operator in strips and cylinders under small localized perturbations. We construct asymptotic approximations for the eigenvalues.

Keywords: Schrodinger operator, waveguide, perturbation, spectrum, asymptotic approximation.

Received: 16.02.2005

English version:
Theoretical and Mathematical Physics, 2005, Volume 145, Issue 3, Pages 1678–1690
DOI: https://doi.org/10.1007/s11232-005-0190-y

Bibliographic databases:

Language: Russian

Citation: R. R. Gadyl'shin, “Local Perturbations of Quantum Waveguides”, TMF, 145:3 (2005), 358–371; Theoret. and Math. Phys., 145:3 (2005), 1678–1690

Citation in format AMSBIB

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Linking options:

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https://doi.org/10.4213/tmf1905

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This publication is cited in the following 34 articles:

S. A. Nazarov, “The preservation of threshold resonances and the splitting off of eigenvalues from the threshold of the continuous spectrum of quantum waveguides”, Sb. Math., 212:7 (2021), 965–1000
S. A. Nazarov, “Threshold resonances and virtual levels in the spectrum of cylindrical and periodic waveguides”, Izv. Math., 84:6 (2020), 1105–1160
Cardone G., Durante T., Nazarov S.A., “Embedded Eigenvalues of the Neumann Problem in a Strip With a Box-Shaped Perturbation”, J. Math. Pures Appl., 112 (2018), 1–40
Piat V.Ch., Nazarov S.A., Taskinen J., “Embedded Eigenvalues Forwater-Waves in Athree-Dimensional Channel With Athin Screen”, Q. J. Mech. Appl. Math., 71:2 (2018), 187–220
S. A. Nazarov, “Transmission of waves through a small aperture in the cross-wall in an acoustic waveguide”, Siberian Math. J., 59:1 (2018), 85–101
S. A. Nazarov, “Asymptotics of eigenvalues in spectral gaps of periodic waveguides with small singular perturbations”, J. Math. Sci. (N. Y.), 243:5 (2019), 746–773
S. A. Nazarov, “Various manifestations of Wood anomalies in locally distorted quantum waveguides”, Comput. Math. Math. Phys., 58:11 (2018), 1838–1855
Lampart J., Teufel S., “The adiabatic limit of Schrödinger operators on fibre bundles”, Math. Ann., 367:3-4 (2017), 1647–1683
I. Kh. Khusnullin, “Vozmuschenie volnovoda uzkim potentsialom”, Tr. IMM UrO RAN, 23, no. 2, 2017, 274–284
Durante T., “Waveguides With a Box-Shaped Perturbation: Eigenvalues of the Neumann Problem”, Proceedings of the International Conference on Numerical Analysis and Applied Mathematics 2016 (ICNAAM-2016), AIP Conference Proceedings, 1863, eds. Simos T., Tsitouras C., Amer Inst Physics, 2017, UNSP 510003-1
S. A. Nazarov, “Almost standing waves in a periodic waveguide with a resonator and near-threshold eigenvalues”, St. Petersburg Math. J., 28:3 (2017), 377–410
Nazarov S.A., Ruotsalainen K.M., Silvola M., “Trapped Modes in Piezoelectric and Elastic Waveguides”, J. Elast., 124:2 (2016), 193–223
Bikmetov A.R. Gadyl'shin R.R., “On local perturbations of waveguides”, Russ. J. Math. Phys., 23:1 (2016), 1–18
S. A. Nazarov, “Transmission Conditions in One-Dimensional Model of a Rectangular Lattice of Thin Quantum Waveguides”, J Math Sci, 219:6 (2016), 994
Nazarov S.A., Ruotsalainen K., Uusitalo P., “Bound States of Waveguides With Two Right-Angled Bends”, J. Math. Phys., 56:2 (2015), 021505
S. A. Nazarov, “Scattering anomalies in a resonator above the thresholds of the continuous spectrum”, Sb. Math., 206:6 (2015), 782–813
Nazarov S.A., “Near-threshold effects of the scattering of waves in a distorted elastic two-dimensional waveguide”, Pmm-J. Appl. Math. Mech., 79:4 (2015), 374–387
S. A. Nazarov, “Bounded solutions in a $\mathrm{T}$ -shaped waveguide and the spectral properties of the Dirichlet ladder”, Comput. Math. Math. Phys., 54:8 (2014), 1261–1279
Cardone G., Nazarov S.A., Ruotsalainen K., “Bound States of a Converging Quantum Waveguide”, ESAIM-Math. Model. Numer. Anal.-Model. Math. Anal. Numer., 47:1 (2013), 305–315
S. A. Nazarov, “Enforced Stability of a Simple Eigenvalue in the Continuous Spectrum of a Waveguide”, Funct. Anal. Appl., 47:3 (2013), 195–209

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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