Ground States of One-Dimensional Fermionic Schrödinger Systems Near a Critical Exponent
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913045213609984 |
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| author | Chen, Bin Guo, Yujin Luo, Yong Wei, Juncheng |
| author_facet | Chen, Bin Guo, Yujin Luo, Yong Wei, Juncheng |
| contents | We study ground states of the fermionic nonlinear Schrödinger system $J_2(p)$ in $\R$, where $p>1$ denotes a polynomial exponent of the nonlinear term. It is known that the system $J_2(p)$ admits ground states for any $1<p<2$, while there is no ground state for $J_2(2)$. We prove that there is no ground state of $J_2(p)$ as $p\searrow 2$, which addresses the special case of Conjecture 5 in [D. Gontier, M. Lewin and F. Q. Nazar, ARMA, 2021]. The refined limiting profile of ground states for $J_2(p)$ is also analyzed as $p\nearrow 2$, which shows that the corresponding density admits exactly two bumps whose distance goes up to infinity as $p\nearrow 2$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_17363 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Ground States of One-Dimensional Fermionic Schrödinger Systems Near a Critical Exponent Chen, Bin Guo, Yujin Luo, Yong Wei, Juncheng Analysis of PDEs 34E05, 81V74 We study ground states of the fermionic nonlinear Schrödinger system $J_2(p)$ in $\R$, where $p>1$ denotes a polynomial exponent of the nonlinear term. It is known that the system $J_2(p)$ admits ground states for any $1<p<2$, while there is no ground state for $J_2(2)$. We prove that there is no ground state of $J_2(p)$ as $p\searrow 2$, which addresses the special case of Conjecture 5 in [D. Gontier, M. Lewin and F. Q. Nazar, ARMA, 2021]. The refined limiting profile of ground states for $J_2(p)$ is also analyzed as $p\nearrow 2$, which shows that the corresponding density admits exactly two bumps whose distance goes up to infinity as $p\nearrow 2$. |
| title | Ground States of One-Dimensional Fermionic Schrödinger Systems Near a Critical Exponent |
| topic | Analysis of PDEs 34E05, 81V74 |
| url | https://arxiv.org/abs/2604.17363 |