On stability of rotational 2D binary Bose-Einstein condensates

Rémi Carles (1) , Van Duong Dinh (2, 3) , Hichem Hajaiej (4)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 Department of Mathematics
4 CAL STATE LA - California State University [Los Angeles]

We consider a two-dimensional nonlinear Schrödinger equation proposed in Physics to model rotational binary Bose-Einstein condensates. The nonlinearity is a logarithmic modification of the usual cubic nonlinearity. The presence of both the external confining potential and rotating frame makes it difficult to apply standard techniques to directly construct ground states, as we explain in an appendix. The goal of the present paper is to analyze the orbital stability of the set of energy minimizers under mass constraint, according to the relative strength of the confining potential compared to the angular frequency. The main novelty concerns the critical case (lowest Landau Level) where these two effects compensate exactly, and orbital stability is established by using techniques related to magnetic Schrödinger operators.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Rémi Carles, Van Duong Dinh, Hichem Hajaiej. On stability of rotational 2D binary Bose-Einstein condensates. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2023, 32 (1), pp.81-124. ⟨10.5802/afst.1730⟩. ⟨hal-02965508v2⟩