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Ground states of attractive Bose gases near the critical rotating velocity.
- Source :
- Calculus of Variations & Partial Differential Equations; Sep2023, Vol. 62 Issue 7, p1-31, 31p
- Publication Year :
- 2023
-
Abstract
- We study ground states of attractive Bose gases, which are confined in a harmonic trap V (x) = x 1 2 + Λ x 2 2 ( Λ ≥ 1 ) rotating at the velocity Ω . For any 0 ≤ Ω < Ω ∗ : = 2 , where Ω ∗ is called a critical rotational velocity, it is well known that ground states exist if and only if a < a ∗ for some critical constant 0 < a ∗ < ∞ , where a > 0 denotes the product for the number of particles times the absolute value of the scattering length. In this paper, we consider the critical rotating case, where the rotational velocity Ω = Ω ∗ , to study the existence and non-existence of ground states with respect to a > 0 . As imposed in Remark 2.2 of Lewin et al. (Blow-up profile of rotating 2D focusing bose gases. macroscopic limits of quantum systems, Springer, Berlin, 2018), we also analyze the limiting behavior of ground states as a ↗ a ∗ for the case where Ω = Ω a : = Ω ∗ 1 - C 0 (a ∗ - a) m ↗ Ω ∗ , 0 ≤ m < 1 2 and 0 < C 0 < 1 . [ABSTRACT FROM AUTHOR]
- Subjects :
- BOSE-Einstein gas
CRITICAL velocity
SCATTERING (Physics)
ABSOLUTE value
Subjects
Details
- Language :
- English
- ISSN :
- 09442669
- Volume :
- 62
- Issue :
- 7
- Database :
- Complementary Index
- Journal :
- Calculus of Variations & Partial Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 170040808
- Full Text :
- https://doi.org/10.1007/s00526-023-02547-x