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The Landau Hamiltonian with delta-potentials supported on curves
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SYSNO ASEP 0524523 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The Landau Hamiltonian with delta-potentials supported on curves Author(s) Behrndt, J. (AT)
Exner, Pavel (UJF-V) RID, ORCID, SAI
Holzmann, M. (AT)
Lotoreichik, Vladimir (UJF-V) ORCID, SAINumber of authors 4 Article number 2050010 Source Title Reviews in Mathematical Physics - ISSN 0129-055X
Roč. 32, č. 4 (2020)Number of pages 51 s. Publication form Print - P Language eng - English Country SG - Singapore Keywords Landau Hamiltonian ; magnetic Schrodinger operator ; singular perturbation ; delta-potential ; eigenvalue clustering ; spectral asymptotics ; Toeplitz operator ; approximation by regular potentials Subject RIV BE - Theoretical Physics OECD category Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) R&D Projects 7AMB17AT022 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) GA17-01706S GA ČR - Czech Science Foundation (CSF) Method of publishing Limited access Institutional support UJF-V - RVO:61389005 UT WOS 000531487500002 EID SCOPUS 85073877359 DOI 10.1142/S0129055X20500105 Annotation The spectral properties of the singularly perturbed self-adjoint Landau Hamiltonian A(alpha) = (i del + A)(2) + alpha delta(Sigma) in L-2(R-2) with a delta-potential supported on a finite C-1,C-1-smooth curve Sigma are studied. Here A = 1/2 B(-x(2), x(1))(T) is the vector potential, B > 0 is the strength of the homogeneous magnetic field, and alpha is an element of L-infinity(Sigma) is a position-dependent real coefficient modeling the strength of the singular interaction on the curve Sigma. After a general discussion of the qualitative spectral properties of A(alpha) and its resolvent, one of the main objectives in the present paper is a local spectral analysis of A(alpha) near the Landau levels B(2q + 1), q is an element of N-0. Under various conditions on alpha, 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 alpha. Furthermore, the use of Landau Hamiltonians with delta-perturbations as model operators for more realistic quantum systems is justified by showing that A(alpha) can be approximated in the norm resolvent sense by a family of Landau Hamiltonians with suitably scaled regular potentials. Workplace Nuclear Physics Institute Contact Markéta Sommerová, sommerova@ujf.cas.cz, Tel.: 266 173 228 Year of Publishing 2021 Electronic address https://doi.org/10.1142/S0129055X20500105
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