Optimization of the lowest eigenvalue of a soft quantum ring

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F21%3A00541787" target="_blank" >RIV/61389005:_____/21:00541787 - isvavai.cz</a>
Alternative codes found
RIV/68407700:21340/21:00355925
Result on the web
<a href="https://doi.org/10.1007/s11005-021-01369-2" target="_blank" >https://doi.org/10.1007/s11005-021-01369-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s11005-021-01369-2" target="_blank" >10.1007/s11005-021-01369-2</a>

Result language
angličtina
Original language name
Optimization of the lowest eigenvalue of a soft quantum ring
Original language description
We consider the self-adjoint two-dimensional Schrodinger operator H-mu associated with the differential expression - Delta - mu describing a particle exposed to an attractive interaction given by ameasure mu supported in a closed curvilinear strip and having fixed transversal one-dimensional profilemeasure mu(perpendicular to). This operator has nonempty negative discrete spectrum, and we obtain two optimization results for its lowest eigenvalue. For the first one, we fix mu(perpendicular to) and maximize the lowest eigenvalue with respect to shape of the curvilinear strip, the optimizer in the first problem turns out to be the annulus. We also generalize this result to the situationwhich involves an additional perturbation of H-mu in the form of a positive multiple of the characteristic function of the domain surrounded by the curvilinear strip. Secondly, we fix the shape of the curvilinear strip and minimize the lowest eigenvalue with respect to variation of mu(perpendicular to), under the constraint that the total profile measure alpha > 0 is fixed. The optimizer in this problem is mu(perpendicular to) given by the product of alpha and the Dirac delta-function supported at an optimal position.
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
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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