Abstract:
The model Neuman Laplacian in the system of two resonators, connected through a thin channel, is studied. The first terms of the asymptotic expansions of eigenvalues and eigenfunctions by small linking parameter are obtained. An explicit expression for resolvent is derived. The model problem is compared to a real one.
Citation:
A. A. Kiselev, B. S. Pavlov, “The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators”, TMF, 100:3 (1994), 354–366; Theoret. and Math. Phys., 100:3 (1994), 1065–1074
\Bibitem{KisPav94}
\by A.~A.~Kiselev, B.~S.~Pavlov
\paper The eigenvalues and eigenfunctions of Laplas operator with Neuman boundary conditions in the system of two connected resonators
\jour TMF
\yr 1994
\vol 100
\issue 3
\pages 354--366
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1311894}
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\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 100
\issue 3
\pages 1065--1074
\crossref{https://doi.org/10.1007/BF01018571}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1994QP25500005}
Linking options:
https://www.mathnet.ru/eng/tmf1654
https://www.mathnet.ru/eng/tmf/v100/i3/p354
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Vorobiev A.M. Trifanova E.S. Popov I.Y., “Resonance Asymptotics For a Pair Quantum Waveguides With Common Semitransparent Perforated Wall”, Nanosyst.-Phys. Chem. Math., 11:6 (2020), 619–627
Vorobiev A.M. Bagmutov A.S. Popov I A., “On Formal Asymptotic Expansion of Resonance For Quantum Waveguide With Perforated Semitransparent Barrier”, Nanosyst.-Phys. Chem. Math., 10:4 (2019), 415–419
Dozyslav B. Kuryliak, Zinoviy Theodorovych Nazarchuk, Oksana B. Trishchuk, “AXIALLY-SYMMETRIC TM-WAVES DIFFRACTION BY SPHERE-CONICAL CAVITY”, PIER B, 73 (2017), 1
R. R. Gadyl'shin, “On the eigenvalues of a “dumb-bell with a thin handle””, Izv. Math., 69:2 (2005), 265–329
Pavlov, BS, “Possible construction of a quantum multiplexer”, Europhysics Letters, 52:2 (2000), 196
V.A. Geyler, I.Yu. Popov, S.L. Popova, “Transmission coefficient for ballistic transport through quantum resonator”, Reports on Mathematical Physics, 40:3 (1997), 531
Alexander Kiselev, “Some Examples in One-Dimensional “Geometric” Scattering on Manifolds”, Journal of Mathematical Analysis and Applications, 212:1 (1997), 263
R. R. Gadyl'shin, “On scattering by cylinder with narrow slit and with shell of finite depth”, Theoret. and Math. Phys., 106:1 (1996), 19–34
V. A. Geiler, I. Yu. Popov, “Ballistic transport in nanostructures: explicitly solvable models”, Theoret. and Math. Phys., 107:1 (1996), 427–434