Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910384226566144 |
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| author | Guo, Yujin Li, Yan |
| author_facet | Guo, Yujin Li, Yan |
| contents | We study the two-spinless mass-critical Fermi systems with attractive interactions and trapping potentials. We prove that ground states of the system exist, if and only if the strength $a$ of attractive interactions satisfies $0<a<a_2^*$, where $0<a_2^*<+\infty$ is the best constant of a dual finite-rank Lieb-Thirring inequality. By the blow-up analysis of many-fermion systems, we show that ground states of the system concentrate at the flattest minimum points of the trapping potential $V(x)$ as $a\nearrow a_2^*$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2403_17591 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions Guo, Yujin Li, Yan Mathematical Physics Functional Analysis We study the two-spinless mass-critical Fermi systems with attractive interactions and trapping potentials. We prove that ground states of the system exist, if and only if the strength $a$ of attractive interactions satisfies $0<a<a_2^*$, where $0<a_2^*<+\infty$ is the best constant of a dual finite-rank Lieb-Thirring inequality. By the blow-up analysis of many-fermion systems, we show that ground states of the system concentrate at the flattest minimum points of the trapping potential $V(x)$ as $a\nearrow a_2^*$. |
| title | Mass Concentration of Two-Spinless Fermi Systems with Attractive Interactions |
| topic | Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2403.17591 |