The Landau Hamiltonian with delta-potentials supported on curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F20%3A00524523" target="_blank" >RIV/61389005:_____/20:00524523 - 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 delta-potentials supported on curves
Original language description
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.
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
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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