A separation threshold for ground states of two-component attractive Bose--Einstein condensates in displaced harmonic traps
Abstract
In this paper, we study the existence of ground states for two-component attractive Bose--Einstein condensates with displaced harmonic trapping potentials V1(x)=|x−x1|2 and V2(x)=|x−x2|2, where x1≠ x2∈ℝ2. For intraspecies interactions a1,a2∈ (0,a*), we focus on the critical interspecies coupling β=β*:=a*+√((a*−a1)(a*−a2)) and prove that there exists a separation threshold dc∈(0,∞) such that the corresponding constrained minimization problem admits no minimizer when 0<|x1−x2|<dc, whereas it admits a minimizer when |x1−x2|≥ dc. The threshold is given by dc=Λ*−1/4, where Λ* is characterized by an auxiliary variational problem and attained. Our results extend the previous work of Guo et al. [J. Funct. Anal. 276 (2019)] and complete the existence classification of ground states for two-component attractive Bose--Einstein condensates with harmonic trapping potentials.
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BibTeX
@misc{yu2026separation,
title = {{A separation threshold for ground states of two-component attractive Bose--Einstein condensates in displaced harmonic traps}},
author = {Shubin Yu and Chun-Lei Tang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05183},
eprint = {2610.05183},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05183},
}
RIS
TY - UNPB
TI - A separation threshold for ground states of two-component attractive Bose--Einstein condensates in displaced harmonic traps
AU - Shubin Yu
AU - Chun-Lei Tang
PY - 2026
DA - 2026/10/04
PB - arXiv
DO - 10.48550/arxiv.2610.05183
UR - https://arxiv.org/abs/2610.05183
AB - In this paper, we study the existence of ground states for two-component attractive Bose--Einstein condensates with displaced harmonic trapping potentials V_1(x)=|x−x_1|^2 and V_2(x)=|x−x_2|^2, where x_1≠ x_2∈ℝ^2. For intraspecies interactions a_1,a_2∈ (0,a^*), we focus on the critical interspecies coupling β=β^*:=a^*+√((a^*−a_1)(a^*−a_2)) and prove that there exists a separation threshold d_c∈(0,∞) such that the corresponding constrained minimization problem admits no minimizer when 0<|x_1−x_2|<d_c, whereas it admits a minimizer when |x_1−x_2|≥ d_c. The threshold is given by d_c=Λ_*^−1/4, where Λ_* is characterized by an auxiliary variational problem and attained. Our results extend the previous work of Guo et al. [J. Funct. Anal. 276 (2019)] and complete the existence classification of ground states for two-component attractive Bose--Einstein condensates with harmonic trapping potentials.
ER -