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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2018

Derivation of the dipolar Gross-Pitaevskii energy

Résumé

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.
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hal-01486983 , version 1 (10-03-2017)

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Arnaud Triay. Derivation of the dipolar Gross-Pitaevskii energy. SIAM Journal on Mathematical Analysis, 2018, ⟨10.1137/17M112378X⟩. ⟨hal-01486983⟩
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