Spectral transitions for Aharonov-Bohm Laplacians on conical layers
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F19%3A00522298" target="_blank" >RIV/61389005:_____/19:00522298 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/19:00326305
Result on the web
<a href="https://doi.org/10.1017/prm.2018.64" target="_blank" >https://doi.org/10.1017/prm.2018.64</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/prm.2018.64" target="_blank" >10.1017/prm.2018.64</a>
Alternative languages
Result language
angličtina
Original language name
Spectral transitions for Aharonov-Bohm Laplacians on conical layers
Original language description
We consider the Laplace operator in a tubular neighbourhood of a conical surface of revolution, subject to an Aharonov-Bohm magnetic field supported on the axis of symmetry and Dirichlet boundary conditions on the boundary of the domain. We show that there exists a critical total magnetic flux depending on the aperture of the conical surface for which the system undergoes an abrupt spectral transition from infinitely many eigenvalues below the essential spectrum to an empty discrete spectrum. For the critical flux, we establish a Hardy-type inequality. In the regime with an infinite discrete spectrum, we obtain sharp spectral asymptotics with a refined estimate of the remainder and investigate the dependence of the eigenvalues on the aperture of the surface and the flux of the magnetic field.
Czech name
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Czech description
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Classification
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)
Result continuities
Project
<a href="/en/project/GA18-08835S" target="_blank" >GA18-08835S: Quantum mechanics with non-self-adjoint operators: transition from spectra to pseudospectra</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Proceedings of the Royal Society of Edinburgh. A - Mathematics
ISSN
0308-2105
e-ISSN
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Volume of the periodical
149
Issue of the periodical within the volume
6
Country of publishing house
GB - UNITED KINGDOM
Number of pages
25
Pages from-to
1663-1687
UT code for WoS article
000512932300016
EID of the result in the Scopus database
2-s2.0-85060636978