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Morizot, O., Colombe, Y., Lorent, V., Perrin, H. and Garraway, B.M. (2006) Ring Trap for Ultracold Atoms. Physical Review A, 74, Article 023617.
https://doi.org/10.1103/physreva.74.023617

has been cited by the following article:

• TITLE: Normalized Solutions to a Planar Schrödinger-Poisson System with Ring-Shaped Potentials and Inhomogeneous Interactions

  AUTHORS: Xuanxuan Li

  KEYWORDS: Schrödinger-Poisson System, Normalized Solution, Logarithmic Convolution, Ringed-Shaped Potential

  JOURNAL NAME: Open Access Library Journal, Vol.13 No.8, August 25, 2026

  ABSTRACT: This paper studies the constrained minimization problem for the Schrödinger-Poisson system with a ring-shaped potential and a logarithmic convolution term in ℝ 2 . The energy functional is made well-defined by introducing a weighted Sobolev space X and decomposing the logarithmic kernel. Define the critical constant a * = | Q | 2 2 , where Q is the unique positive radially symmetric solution of the two-dimensional scalar field equation −Δu+u= u 3 . Under suitable assumptions on the interaction coefficient K( x ) , the existence and nonexistence of minimizers for the minimization problem e( γ,a ) are systematically studied. The main results show that minimizers exist when a< a * and do not exist when a> a * or a= a * (with γ>0 ). Furthermore, for γ>0 , the asymptotic behavior of minimizers is characterized as a↗ a * .