Ground States of a Coupled Fractional Schrödinger System under a Total-Mass Constraint: Complete Classification and Concentration Behavior
Abstract
We consider a coupled fractional Schrödinger system with trapping potentials under a total-mass constraint, in which both the intraspecies and the interspecies interactions are attractive. For every fractional order s∈(0,1) and dimension N≥1, we obtain a complete classification of the existence and non-existence of minimizers: minimizers exist if and only if both intraspecies coefficients lie below the single-component critical mass and the interspecies coupling coefficient lies below an explicit critical threshold β*, and no minimizer exists otherwise. The threshold β* is characterized by means of an auxiliary intensity function, which yields a lower bound for the energy functional without invoking a new coupled Gagliardo--Nirenberg inequality. As the coupling coefficient approaches β*, we analyze the concentration behavior. In the one-dimensional half-Laplacian case, the two components are shown to blow up at a common zero of the trapping potentials and, after rescaling, to converge to the same fractional ground-state profile, with the mass ratio determined explicitly by the intraspecies coefficients and the critical mass. For polynomial trapping potentials whose flattest common zero has order q0∈(0,1), the sharp blow-up rate is established, and both components concentrate simultaneously at the flattest common minimum.
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BibTeX
@misc{liu2026ground,
title = {{Ground States of a Coupled Fractional Schrödinger System under a Total-Mass Constraint: Complete Classification and Concentration Behavior}},
author = {Lijun Liu and Jiabin Zuo},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00520},
eprint = {2611.00520},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00520},
note = {CC0},
}
RIS
TY - UNPB
TI - Ground States of a Coupled Fractional Schrödinger System under a Total-Mass Constraint: Complete Classification and Concentration Behavior
AU - Lijun Liu
AU - Jiabin Zuo
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00520
UR - https://arxiv.org/abs/2611.00520
AB - We consider a coupled fractional Schrödinger system with trapping potentials under a total-mass constraint, in which both the intraspecies and the interspecies interactions are attractive. For every fractional order s∈(0,1) and dimension N≥1, we obtain a complete classification of the existence and non-existence of minimizers: minimizers exist if and only if both intraspecies coefficients lie below the single-component critical mass and the interspecies coupling coefficient lies below an explicit critical threshold β^*, and no minimizer exists otherwise. The threshold β^* is characterized by means of an auxiliary intensity function, which yields a lower bound for the energy functional without invoking a new coupled Gagliardo--Nirenberg inequality. As the coupling coefficient approaches β^*, we analyze the concentration behavior. In the one-dimensional half-Laplacian case, the two components are shown to blow up at a common zero of the trapping potentials and, after rescaling, to converge to the same fractional ground-state profile, with the mass ratio determined explicitly by the intraspecies coefficients and the critical mass. For polynomial trapping potentials whose flattest common zero has order q_0∈(0,1), the sharp blow-up rate is established, and both components concentrate simultaneously at the flattest common minimum.
ER -