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Derivation of the Time Dependent Gross-Pitaevskii Equation Without Positivity Condition on the Interaction

dc.contributor.author Pickl, P
dc.date.accessioned 2018-06-04T15:43:51Z
dc.date.available 2018-06-04T15:43:51Z
dc.date.issued 2010-07
dc.identifier.issn 0022-4715
dc.identifier.issn 1572-9613
dc.identifier.uri https://hdl.handle.net/10161/17114
dc.description.abstract Using a new method (Pickl in A simple derivation of mean field limits for quantum systems, 2010) it is possible to derive mean field equations from the microscopic N body Schrödinger evolution of interacting particles without using BBGKY hierarchies. In this paper we wish to analyze scalings which lead to the Gross-Pitaevskii equation which is usually derived assuming positivity of the interaction (Erdös et al. in Commun. Pure Appl. Math. 59(12):1659-1741, 2006; Invent. Math. 167:515-614, 2007). The new method for dealing with mean field limits presented in Pickl (2010) allows us to relax this condition. The price we have to pay for this relaxation is however that we have to restrict the scaling behavior of the interaction and that we have to assume fast convergence of the reduced one particle marginal density matrix of the initial wave function μ Ψ0 to a pure state {pipe}φ 0 〉〈φ 0 {pipe}. © 2010 Springer Science+Business Media, LLC.
dc.publisher Springer Science and Business Media LLC
dc.relation.ispartof Journal of Statistical Physics
dc.relation.isversionof 10.1007/s10955-010-9981-0
dc.subject Mean field limits
dc.subject Gross-Pitaevskii equation
dc.subject BEC
dc.title Derivation of the Time Dependent Gross-Pitaevskii Equation Without Positivity Condition on the Interaction
dc.type Journal article
duke.contributor.id Pickl, P|0877677
dc.date.updated 2018-06-04T15:43:50Z
pubs.issue 1
pubs.organisational-group Duke Kunshan University
pubs.organisational-group Duke
pubs.organisational-group Duke Kunshan University Faculty
pubs.publication-status Published
pubs.volume 140


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