Optimization of the lowest eigenvalue of a soft quantum ring

0541787 - ÚJF 2022 RIV NL eng J - Článek v odborném periodiku
Exner, Pavel - Lotoreichik, Vladimir
Optimization of the lowest eigenvalue of a soft quantum ring.
Letters in Mathematical Physics. Roč. 111, č. 2 (2021), č. článku 28. ISSN 0377-9017. E-ISSN 1573-0530
Grant CEP: GA ČR(CZ) GA21-07129S
Institucionální podpora: RVO:61389005
Klíčová slova: lowest eigenvalue * Eigenvalue optimization * soft quantum ring
Obor OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Impakt faktor: 1.520, rok: 2021
Způsob publikování: Omezený přístup
https://doi.org/10.1007/s11005-021-01369-2

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.
Trvalý link: http://hdl.handle.net/11104/0319320