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Article Dans Une Revue SIAM Journal on Mathematical Analysis Année : 2019

On the stability of 2D dipolar Bose-Einstein condensates

Résumé

We study the existence of energy minimizers for a Bose-Einstein condensate with dipole-dipole interactions, tightly confined to a plane. The problem is critical in that the kinetic energy and the (partially attractive) interaction energy behave the same under mass-preserving scalings of the wave-function. We obtain a sharp criterion for the existence of ground states, involving the optimal constant of a certain generalized Gagliardo-Nirenberg inequality.
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Dates et versions

hal-01875565 , version 1 (17-09-2018)
hal-01875565 , version 2 (25-09-2018)
hal-01875565 , version 3 (01-02-2019)

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Arnaud Eychenne, Nicolas Rougerie. On the stability of 2D dipolar Bose-Einstein condensates. SIAM Journal on Mathematical Analysis, 2019, 51 (2), ⟨10.1137/18M1216663⟩. ⟨hal-01875565v3⟩
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