The Nonexistence of Vortices for Rotating Bose–Einstein Condensates with Attractive Interactions

Guo, Yujin; Luo, Yong; Yang, Wen

doi:10.1007/s00205-020-01564-w

Cited by 33 publications

(57 citation statements)

References 55 publications

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“…Such type of limit behavior of minimizers corresponding to global minimization problems arising in two-dimensional Bose-Einstein condensate are well studied, see e.g. [13,14] and the references therein. Concerning with local minimization problems, this type of results is new, as far as we know.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Luo¹,

Stylianou²

2021

DCDS-B

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We study the following nonlocal mixed order Gross-Pitaevskii equation i ∂tψ = − 1 2 ∆ψ + Vext ψ + λ 1 |ψ| 2 ψ + λ 2 (K * |ψ| 2) ψ + λ 3 |ψ| p−2 ψ, where K is the classical dipole-dipole interaction kernel, λ 3 > 0 and p ∈ (4, 6]; the case p = 6 being energy critical. For p = 5 the equation is considered currently as the state-of-the-art model for describing the dynamics of dipolar Bose-Einstein condensates (Lee-Huang-Yang corrected dipolar GPE). We prove existence and nonexistence of standing waves in different parameter regimes; for p = 6 we prove global well-posedness and small data scattering.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Luo¹,

Stylianou²

2021

DCDS-B

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“…Subsequently, [6] proved the stability of complexvalued minimizers for I(ρ) in R 3 . Recently, much attention has been attracted to the problem I(ρ) again due to its significance on rotating BEC theory [2,17,18,25].…”

Section: Introductionmentioning

confidence: 99%

“…According to [25], the model of two dimensional rotating BEC can be described by the L 2 −critical version of I(ρ), for which the exponent 1 < p < 3 was replaced by p = 3 in the functional E ρ (u). For this L 2 −critical problem, [18,25] proved that there exist critical constants 0 < Ω * := Ω * (V ) ≤ ∞ and ρ * > 0, such that for any Ω ∈ (0, Ω * ), minimizers of I(ρ) exist if and only if ρ < ρ * . Moreover, by developing the method of inductive symmetry, [18] also proved the uniqueness and free-vortex of minimizers for I(ρ) as ρ ր ρ * for some suitable class of radial potential V (x) = V (|x|).…”

Section: Introductionmentioning

confidence: 99%

“…For this L 2 −critical problem, [18,25] proved that there exist critical constants 0 < Ω * := Ω * (V ) ≤ ∞ and ρ * > 0, such that for any Ω ∈ (0, Ω * ), minimizers of I(ρ) exist if and only if ρ < ρ * . Moreover, by developing the method of inductive symmetry, [18] also proved the uniqueness and free-vortex of minimizers for I(ρ) as ρ ր ρ * for some suitable class of radial potential V (x) = V (|x|). More recently, the authors in [17] have generalized the local uniqueness result of [18] to the non-radially symmetric case of V (x).…”

Section: Introductionmentioning

confidence: 99%

“…Moreover, by developing the method of inductive symmetry, [18] also proved the uniqueness and free-vortex of minimizers for I(ρ) as ρ ր ρ * for some suitable class of radial potential V (x) = V (|x|). More recently, the authors in [17] have generalized the local uniqueness result of [18] to the non-radially symmetric case of V (x).…”

Section: Introductionmentioning

confidence: 99%

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Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

Gao¹,

Luo²

2021

Preprint

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This paper considers ground states of mass subcritical rotational nonlinear Schrödinger equationwhere V (x) is an external potential, Ω > 0 characterizes the rotational velocity of the trap V (x), 1 < p < 3 and ρ > 0 describes the strength of the attractive interactions. It is shown that ground states of the above equation can be described equivalently by minimizers of the L 2 − constrained variational problem. We prove that minimizers exist for any ρ ∈ (0, ∞) when 0 < Ω < Ω * , where 0 < Ω * := Ω * (V ) < ∞ denotes the critical rotational velocity of V (x). While Ω > Ω * , there admits no minimizers for any ρ ∈ (0, ∞). For fixed 0 < Ω < Ω * , by using energy estimates and blow-up analysis, we also analyze the limit behavior of minimizers as ρ → ∞. Finally, we prove that up to a constant phase, there exists a unique minimizer when ρ > 0 is large enough and Ω ∈ (0, Ω * ) is fixed.

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Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation

Basharat

Hajaiej

et al. 2022

Ann. Henri Poincaré

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The Nonexistence of Vortices for Rotating Bose–Einstein Condensates with Attractive Interactions

Cited by 33 publications

References 55 publications

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

On 3d dipolar Bose-Einstein condensates involving quantum fluctuations and three-body interactions

Mass concentration and uniqueness of ground states for mass subcritical rotational nonlinear Schrödinger equations

Threshold for Blowup and Stability for Nonlinear Schrödinger Equation with Rotation

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