10.1007/s00220-019-03599-x
Jeblick, Maximilian
Maximilian
Jeblick
Leopold, Nikolai K
Nikolai K
Leopold0000-0002-0495-6822
Pickl, Peter
Peter
Pickl
Derivation of the time dependent Gross–Pitaevskii equation in two dimensions
Springer Nature
2019
2019-11-25T08:08:02Z
2020-01-16T12:38:17Z
journal_article
https://research-explorer.app.ist.ac.at/record/7100
https://research-explorer.app.ist.ac.at/record/7100.json
0010-3616
884469 bytes
application/pdf
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.