Critical surface for two component Bose-Einstein Condensates
Abstract
We investigate the existence of ground states for two-component Bose--Einstein condensates with intraspecies interactions a1, a2 ∈ (0, a*) and interspecies interaction β>0. By carefully investigating an associated auxiliary minimization problem, we prove the existence of a unique, continuous, critical surface γ= γ(a1, a2) between β*:= √((a* − a1) (a* − a2)) and β*:= a* − (a1 + a2)/2. This surface provides a complete classification for the existence of minimizers: ground states exist for β∈ (0,γ) and do not exist for β> γ. Additionally, when the trapping potentials are continuous at a common zero point, there is no ground state for β= γ. Our results close the gap case β∈ [β*, β*] when a1≠ a2 in literature, significantly extending the results in \cite{Bao-Cai-1,guoBlowupSolutionsTwo2017a}.
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BibTeX
@misc{peng2026critical,
title = {{Critical surface for two component Bose-Einstein Condensates}},
author = {Wenshuai Peng and Xiaoyu Zeng and Qidi Zhang and Huan-Song Zhou},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.27316},
eprint = {2609.27316},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.27316},
}
RIS
TY - UNPB
TI - Critical surface for two component Bose-Einstein Condensates
AU - Wenshuai Peng
AU - Xiaoyu Zeng
AU - Qidi Zhang
AU - Huan-Song Zhou
PY - 2026
DA - 2026/09/23
PB - arXiv
DO - 10.48550/arxiv.2609.27316
UR - https://arxiv.org/abs/2609.27316
AB - We investigate the existence of ground states for two-component Bose--Einstein condensates with intraspecies interactions a_1, a_2 ∈ (0, a^*) and interspecies interaction β>0. By carefully investigating an associated auxiliary minimization problem, we prove the existence of a unique, continuous, critical surface γ= γ(a_1, a_2) between β_*:= √((a^* − a_1) (a^* − a_2)) and β^*:= a^* − (a_1 + a_2)/2. This surface provides a complete classification for the existence of minimizers: ground states exist for β∈ (0,γ) and do not exist for β> γ. Additionally, when the trapping potentials are continuous at a common zero point, there is no ground state for β= γ. Our results close the gap case β∈ [β_*, β^*] when a_1≠ a_2 in literature, significantly extending the results in \cite{Bao-Cai-1,guoBlowupSolutionsTwo2017a}.
ER -