About: On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region

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About: On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region Goto Sponge NotDistinct Permalink

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Attributes	Values
rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	Pro Hamiltoniány s jednou bodovou interakcí v omezené oblasti v dimenzi dva a tři odvozujeme podmínky na tvar této, jež maximalizující nejnižší vlastní hodnotu. (cs) We investigate relations between spectral properties of a single-centre point-interaction Hamiltonian describing a particle confined to a bounded domain Omega subset of R-d, d = 2, 3, with a Dirichlet boundary, and the geometry of Omega. For this class of operators, Krein's formula yields an explicit representation of the resolvent in terms of the integral kernel of the unperturbed one, (- Delta(D)(Omega) + z)(-1). We use a moving plane analysis to characterize the behaviour of the ground-state energy of the Hamiltonian with respect to the point-interaction position and the shape of Omega, in particular, we establish some conditions showing how to place the interaction to optimize the principal eigenvalue. We investigate relations between spectral properties of a single-centre point-interaction Hamiltonian describing a particle confined to a bounded domain Omega subset of R-d, d = 2, 3, with a Dirichlet boundary, and the geometry of Omega. For this class of operators, Krein's formula yields an explicit representation of the resolvent in terms of the integral kernel of the unperturbed one, (- Delta(D)(Omega) + z)(-1). We use a moving plane analysis to characterize the behaviour of the ground-state energy of the Hamiltonian with respect to the point-interaction position and the shape of Omega, in particular, we establish some conditions showing how to place the interaction to optimize the principal eigenvalue. (en)
Title	On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region O optimizaci základního stavu pro operátory s jednou bodovou interakcí v omezené oblasti (cs) On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region (en)
skos:prefLabel	On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region O optimizaci základního stavu pro operátory s jednou bodovou interakcí v omezené oblasti (cs) On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region (en)
skos:notation	RIV/61389005:_____/08:00310460!RIV09-AV0-61389005
http://linked.open...avai/riv/aktivita	P Z
http://linked.open...avai/riv/aktivity	P(IAA100480501), P(LC06002), Z(AV0Z10480505)
http://linked.open...iv/cisloPeriodika	6
http://linked.open...vai/riv/dodaniDat	2009
http://linked.open...aciTvurceVysledku	Exner, Pavel
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	384775
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/08:00310460
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Dirichlet boundary; single-centre; point-interaction (en)
http://linked.open.../riv/klicoveSlovo	single-centre Dirichlet boundary point-interaction
http://linked.open...odStatuVydavatele	GB - Spojené království Velké Británie a Severního Irska
http://linked.open...ontrolniKodProRIV	[387111DB1E8C]
http://linked.open...i/riv/nazevZdroje	Journal of Physics A-Mathematical and Theoretical
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	2 (xsd:int)
http://linked.open...vavai/riv/projekt	Doppler Institute for Mathematical Physics and Applied Mathematics Solvable models of nanosystems
http://linked.open...UplatneniVysledku	2008
http://linked.open...v/svazekPeriodika	41
http://linked.open...iv/tvurceVysledku	Exner, Pavel Mantile, A.
http://linked.open...ain/vavai/riv/wos	000252912100019
http://linked.open...n/vavai/riv/zamer	Jaderná fyzika a příbuzné obory v základním, aplikovaném a interdisciplinárním výzkumu
issn	1751-8113
number of pages	15 (xsd:int)
is http://linked.open...avai/riv/vysledek of	On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region On the optimization of the principal eigenvalue for single-centre point-interaction operators in a bounded region

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