--- res: bibo_abstract: - We present microscopic derivations of the defocusing two-dimensional cubic nonlinear Schrödinger equation and the Gross–Pitaevskii equation starting froman interacting N-particle system of bosons. We consider the interaction potential to be given either by Wβ(x)=N−1+2βW(Nβx), for any β>0, or to be given by VN(x)=e2NV(eNx), for some spherical symmetric, nonnegative and compactly supported W,V∈L∞(R2,R). In both cases we prove the convergence of the reduced density corresponding to the exact time evolution to the projector onto the solution of the corresponding nonlinear Schrödinger equation in trace norm. For the latter potential VN we show that it is crucial to take the microscopic structure of the condensate into account in order to obtain the correct dynamics.@eng bibo_authorlist: - foaf_Person: foaf_givenName: Maximilian foaf_name: Jeblick, Maximilian foaf_surname: Jeblick - foaf_Person: foaf_givenName: Nikolai K foaf_name: Leopold, Nikolai K foaf_surname: Leopold foaf_workInfoHomepage: http://www.librecat.org/personId=4BC40BEC-F248-11E8-B48F-1D18A9856A87 orcid: 0000-0002-0495-6822 - foaf_Person: foaf_givenName: Peter foaf_name: Pickl, Peter foaf_surname: Pickl bibo_doi: 10.1007/s00220-019-03599-x bibo_issue: '1' bibo_volume: 372 dct_date: 2019^xs_gYear dct_identifier: - UT:000495193700002 dct_isPartOf: - http://id.crossref.org/issn/0010-3616 - http://id.crossref.org/issn/1432-0916 dct_language: eng dct_publisher: Springer Nature@ dct_title: Derivation of the time dependent Gross–Pitaevskii equation in two dimensions@ ...