The Landau Hamiltonian with δ-potentials supported on curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F20%3A00339702" target="_blank" >RIV/68407700:21340/20:00339702 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1142/S0129055X20500105" target="_blank" >https://doi.org/10.1142/S0129055X20500105</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1142/S0129055X20500105" target="_blank" >10.1142/S0129055X20500105</a>

Result language
angličtina
Original language name
The Landau Hamiltonian with δ-potentials supported on curves
Original language description
The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian Aα = (idel + A)2 + αδ ς in L2(ℝ2) with a δ-potential supported on a finite C1,1-smooth curve ς are studied. Here A = 1 2B(-x2,x1)τ is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and α L) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve. After a general discussion of the qualitative spectral properties of & and its resolvent, one of the main objectives in the present paper is a local spectral analysis of & near the Landau levels B(2q + 1), q ℕ0. Under various conditions on &, it is shown that the perturbation smears the Landau levels into eigenvalue clusters, and the accumulation rate of the eigenvalues within these clusters is determined in terms of the capacity of the support of . Furthermore, the use of Landau Hamiltonians with δ-perturbations as model operators for more realistic quantum systems is justified by showing that A can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials. 2020 World Scientific Publishing Company.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10100 - Mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2020
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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