Optimization of the lowest eigenvalue of a soft quantum ring

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/68407700:21340/21:00355925

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Optimization of the lowest eigenvalue of a soft quantum ring

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Optimization of the lowest eigenvalue of a soft quantum ring

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Letters in Mathematical Physics

ISSN

0377-9017

e-ISSN

1573-0530

Svazek periodika

111

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

22

Strana od-do

28

Kód UT WoS článku

000625133600001

EID výsledku v databázi Scopus

2-s2.0-85102084633