Leaky Quantum Structures

0539549 - ÚJF 2021 RIV RU eng J - Journal Article
Exner, Pavel
Leaky Quantum Structures.
Proceedings of the Steklov Institute of Mathematics. Roč. 311, č. 1 (2020), s. 114-128. ISSN 0081-5438. E-ISSN 1531-8605
Institutional support: RVO:61389005
Keywords : asymptotic expansions * codimension 1 manifolds * Dirac operators * singular Schrödinger operators * spectral properties
OECD category: Pure mathematics
Impact factor: 0.478, year: 2020
Method of publishing: Limited access
https://doi.org/10.1134/S0081543820060073

The paper reviews spectral properties of a class of singular Schrödinger operators with the interaction supported by manifolds or complexes of codimension 1. In particular, the relation of these properties to the geometric setting of the problem is discussed. We describe how these operators 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 briefly describe results on singular perturbations of Dirac operators.
Permanent Link: http://hdl.handle.net/11104/0317266