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Derivation of the dipolar Gross-Pitaevskii energy

Triay, Arnaud (2017), Derivation of the dipolar Gross-Pitaevskii energy, SIAM Journal on mathematical analysis, 50, 1, p. 33-63. 10.1137/17M112378X

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Type
Article accepté pour publication ou publié
Date
2017
Journal name
SIAM Journal on mathematical analysis
Volume
50
Number
1
Series title
Pages
33-63
Publication identifier
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Author(s)
Triay, Arnaud
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Abstract (EN)
We consider N trapped bosons in R 3 interacting via a pair potential w which has a long range of dipolar type. We show the convergence of the energy and of the minimizers for the many-body problem towards those of the dipolar Gross-Pitaevskii functional, when N tends to infinity. In addition to the usual cubic interaction term, the latter has the long range dipolar interaction. Our results hold under the assumption that the two-particle interaction is scaled in the form N 3β−1 w(N β x) for some 0 ≤ β < βmax with βmax = 1/3 + s/(45 + 42s) where s is related to the growth of the trapping potential.
Subjects / Keywords
Dipolar; Bose Gas; Gross-Pitaevskii