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Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction

Triay, Arnaud (2019-04), Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction. https://basepub.dauphine.fr/handle/123456789/19496

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Type
Document de travail / Working paper
External document link
https://hal.archives-ouvertes.fr/hal-02104829
Date
2019-04
Publisher
Cahier de recherche CEREMADE, Université Paris-Dauphine
Series title
Cahier de recherche CEREMADE, Université Paris-Dauphine
Published in
Paris
Pages
10
Metadata
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Author(s)
Triay, Arnaud
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We study the dipolar Gross-Piteavskii functional with the Lee-Huang-Yang (LHY) correction term without trapping potential and in the regime where the dipole-dipole interaction dominates the repulsive short-range interaction. We show that, above a critical mass, the functional admits minimizers and we prove their regularity and exponential decay. We also estimate the critical mass in terms of the parameters of the system.
Subjects / Keywords
Gross-Pitaevskii theory; Lee-Huang-Yang correction