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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2020, Volume 311, Pages 123–139
DOI: https://doi.org/10.4213/tm4142 (Mi tm4142) 		 
Leaky quantum structures

Pavel Exnerab

a Doppler Institute for Mathematical Physics and Applied Mathematics, Czech Technical University in Prague, Břehová 7, 11519 Prague, Czech Republic
b Department of Theoretical Physics, Nuclear Physics Institute, Czech Academy of Sciences, Husinec – Řež, čp. 130, 25068 Řež, Czech Republic
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DOI: https://doi.org/10.4213/tm4142
Abstract: The paper reviews spectral properties of a class of singular Schrödinger operators with the interaction supported by manifolds or complexes of codimension one, in particular, their relations to the geometric setting of the problem. We describe how they can be approximated by operators of other classes and how such approximations can be used. Furthermore, we present asymptotic expansions of the eigenvalues in terms of the parameters characterizing the coupling strength and geometric deformations. We also give an example illustrating the influence of a magnetic field of the Aharonov-Bohm type and describe briefly results about singular perturbation of Dirac operators.
Keywords: singular Schrödinger operators, codimension one manifolds, spectral properties, asymptotic expansions, Dirac operators.
Funding agency Grant number
European Regional Development Fund CZ.02.1.01/0.0/0.0/16 019/0000778
The research was supported in part by the European Union within the project CZ.02.1.01/0.0/0.0/16 019/0000778.
Received: February 4, 2020
Revised: May 7, 2020
Accepted: July 20, 2020
English version:
Proceedings of the Steklov Institute of Mathematics, 2020, Volume 311, Pages 114–128
DOI: https://doi.org/10.1134/S0081543820060073
Bibliographic databases:
Document Type: Article
UDC: 517.984.46+517.984.56+517.984.66
MSC: 81Q10, 35J10, 35P15
Language: Russian
Citation: Pavel Exner, “Leaky quantum structures”, Analysis and mathematical physics, Collected papers. On the occasion of the 70th birthday of Professor Armen Glebovich Sergeev, Trudy Mat. Inst. Steklova, 311, Steklov Math. Inst., Moscow, 2020, 123–139; Proc. Steklov Inst. Math., 311 (2020), 114–128
Citation in format AMSBIB
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\vol 311
\pages 123--139
\publ Steklov Math. Inst.
\publaddr Moscow
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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