---
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_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@
...