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dc.contributor.authorErdos, Laszlo
dc.contributor.authorSchlein, Benjamin
dc.contributor.authorYau, Horng-Tzer
dc.date.accessioned2017-05-18T17:53:03Z
dc.date.issued2010
dc.identifier.citationErdős, László, Benjamin Schlein, and Horng-Tzer Yau. 2010. “Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate.” Annals of Mathematics 172 (1) (June 27): 291–370. doi:10.4007/annals.2010.172.291.en_US
dc.identifier.issn0003-486Xen_US
dc.identifier.urihttp://nrs.harvard.edu/urn-3:HUL.InstRepos:32706729
dc.description.abstractConsider a system of N bosons in three dimensions interacting via a repulsive short range pair potential N²V (N(xi − xj)), where x = (x1,..., xN) denotes the positions of the particles. Let HN denote the Hamiltonian of the system and let ψN,t be the solution to the Schrödinger equation. Suppose that the initial data ψN,0 satisfies the energy condition ⟨ψN,0, H k NψN,0 ⟩ ≤ C k N k for k = 1, 2,.... We also assume that the k-particle density matrices of the initial state are asymptotically factorized as N → ∞. We prove that the k-particle density matrices of ψN,t are also asymptotically factorized and the one particle orbital wave function solves the Gross-Pitaevskii equation, a cubic non-linear Schrödinger equation with the coupling constant given by the scattering length of the potential V. We also prove the same conclusion if the energy condition holds only for k = 1 but the factorization of ψN,0 is assumed in a stronger sense.en_US
dc.description.sponsorshipMathematicsen_US
dc.language.isoen_USen_US
dc.publisherAnnals of Mathematics, Princeton Uen_US
dc.relation.isversionofdoi:10.4007/annals.2010.172.291en_US
dc.relation.hasversionhttps://arxiv.org/abs/math-ph/0606017en_US
dash.licenseOAP
dc.titleDerivation of the Gross-Pitaevskii equation for the dynamics of Bose-Einstein condensateen_US
dc.typeJournal Articleen_US
dc.description.versionAccepted Manuscripten_US
dc.relation.journalAnnals of Mathematicsen_US
dash.depositing.authorYau, Horng-Tzer
dc.date.available2017-05-18T17:53:03Z
dc.identifier.doi10.4007/annals.2010.172.291*
dash.authorsorderedfalse
dash.contributor.affiliatedYau, Horng-Tzer
dash.contributor.affiliatedErdos, Laszlo


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