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Derivation of the dipolar Gross-Pitaevskii energy
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Derivation of the dipolar Gross-Pitaevskii energy
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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 3$\beta$--1 w(N $\beta$ x) for some 0 $\le$ $\beta$ \textless{} $\beta$max with $\beta$max = 1/3 + s/(45 + 42s) where s is related to the growth of the trapping potential.
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Cited by 1 Pith paper
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On the spherical symmetry and finite-range assumptions of the interaction potential in the low energy study of dilute Bose gases
Removes radiality and compact support assumptions on the interaction potential while proving BEC and Bogoliubov spectrum convergence for the 3D torus Bose gas in the Gross-Pitaevskii regime.
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