2024/12/13 by Meng-Hui Wu, Wu, Meng-Hui, Shubin Yu +3
Physics and Astronomy · #35A15 #35B40 #35Q40 #35Q55 #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Gyrotron and Vacuum Electronics Research #Quantum optics and atomic interactions
paper · pdf · doi:10.48550/arxiv.2412.09890
openalex publication_date 2024/12/13 · openalex created_date 2024/12/17 · openalex updated_date 2026/07/28
In this article, we study the existence and asymptotic properties of\nprescribed mass standing waves for the rotating dipolar Gross-Pitaevskii\nequation with a harmonic potential in the unstable regime. This equation arises\nas an effective model describing Bose-Einstein condensate of trapped dipolar\nquantum gases rotating at the speed \Ω. To be precise, we mainly focus on\nthe two cases: the rotational speed 0<\Ω<\Ω* and\n\Ω=\Ω*, where \Ω* is called a critical rotational speed.\nFor the first case, we obtain two different standing waves, one of which is a\nlocal minimizer and can be determined as the ground state, and the other is\nmountain pass type. For the critical case, we rewrite the original problem as a\ndipole Gross-Pitaevskii equation with a constant magnetic field and partial\nharmonic confinement. Under this setting, a local minimizer can also be\nobtained, which seems to be the optimal result. Particularly, in both cases, we\nestablish the mass collapse behavior of the local minimizers. Our results\nextend the work of Dinh (Lett. Math. Phys., 2022) and Luo et al. (J. Differ.\nEqu., 2021) to the non-axially symmetric harmonic potential, and answer the\nopen question proposed by Dinh.\n