Measure concentration and the Schrödinger equation

dc.contributor.authorYserentant, Harry
dc.date.accessioned2023-06-07T09:15:02Z
dc.date.available2023-06-07T09:15:02Z
dc.date.issued2023-03-24
dc.date.updated2023-04-19T18:06:01Z
dc.description.abstractThis talk pursued the aim to represent the solutions of the electronic Schrödinger equation as traces of higher‐dimensional functions. This allows to decouple the electron‐electron interaction potential but comes at the price of a degenerate elliptic operator replacing the Laplace operator on the higher‐dimensional space. The surprising observation is that this operator can without much loss again be substituted by the Laplace operator, the more successful the larger the system under consideration is. This is due to a nontrivial concentration of measure phenomenon that has much to do with the random projection theorem known from probability theory and can, for example, serve as a building block for the construction of iterative methods that map sums of products of orbitals and geminals onto functions of the same type.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2023
dc.identifier.eissn1617-7061
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/18838
dc.identifier.urihttps://doi.org/10.14279/depositonce-17643
dc.language.isoen
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/
dc.subject.ddc500 Naturwissenschaften und Mathematik::510 Mathematik::510 Mathematik
dc.subject.otherSchrödinger equationen
dc.subject.othermeasure concentrationen
dc.subject.otherhigher-dimensional functionsen
dc.subject.otherelectron-electron interaction potentialen
dc.titleMeasure concentration and the Schrödinger equationen
dc.typeArticle
dc.type.versionpublishedVersion
dcterms.bibliographicCitation.articlenumbere202200005
dcterms.bibliographicCitation.doi10.1002/pamm.202200005
dcterms.bibliographicCitation.issue1
dcterms.bibliographicCitation.journaltitlePAMMen
dcterms.bibliographicCitation.originalpublishernameWiley
dcterms.bibliographicCitation.originalpublisherplaceNew York, NY
dcterms.bibliographicCitation.volume22
dcterms.rightsHolder.referenceCreative-Commons-Lizenz
tub.accessrights.dnbfree
tub.affiliationFak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::FG Numerische Analysis partieller Differentialgleichungen
tub.publisher.universityorinstitutionTechnische Universität Berlin

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