Derivation of the time-dependent Gross-Pitaevskii equation for the dipolar gases
Triay, Arnaud (2019-04), Derivation of the time-dependent Gross-Pitaevskii equation for the dipolar gases. https://basepub.dauphine.fr/handle/123456789/19495
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02091613
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series titleCahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)We derive the time-dependent dipolar Gross-Pitaevskii (GP) equation from the N-body Schrödinger equation. More precisely we show a norm approximation for the solution of the many body equation as well as the convergence of its one-body reduced density matrix towards the orthogonal projector onto the solution of the dipolar GP equation. We consider the interpolation regime where interaction potential is scaled like N3β−1w(Nβ(x−y)), the range of validity of β depends on the stability of the ground state problem. In particular we can prove the convergence on the one-body density matrix assuming wˆ≥0 and β<3/8.
Subjects / KeywordsGross-Pitaevskii equation; dipolar gases
Showing items related by title and author.