Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential I: The $L^2$-Subcritical Case
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866914801266982912 |
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| author | Chen, Bin Guo, Yujin |
| author_facet | Chen, Bin Guo, Yujin |
| contents | We consider ground states of the $N$ coupled fermionic nonlinear Schrödinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter $α>0$, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as $α\to\infty$, where the mass concentrates at one of the singular points for the Coulomb potential $V(x)$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_00563 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential I: The $L^2$-Subcritical Case Chen, Bin Guo, Yujin Mathematical Physics We consider ground states of the $N$ coupled fermionic nonlinear Schrödinger systems with the Coulomb potential $V(x)$ in the $L^2$-subcritical case. By studying the associated constraint variational problem, we prove the existence of ground states for the system with any parameter $α>0$, which represents the attractive strength of the non-relativistic quantum particles. The limiting behavior of ground states for the system is also analyzed as $α\to\infty$, where the mass concentrates at one of the singular points for the Coulomb potential $V(x)$. |
| title | Ground States of Fermionic Nonlinear Schrödinger Systems with Coulomb Potential I: The $L^2$-Subcritical Case |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2310.00563 |