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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.01075 |
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| _version_ | 1866911073274167296 |
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| author | Chen, Hongshuo Chen, Li Lee, Jinyeop Sun, Zhiwei |
| author_facet | Chen, Hongshuo Chen, Li Lee, Jinyeop Sun, Zhiwei |
| contents | We explore a system of two-species fermions with $N$ particles. Through this exploration, we establish a two-species Husimi measure and construct a two-species Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy with error terms. We provide proofs of the smallness of these errors in the semiclassical and mean-field limits, fixing $\hbar = N^{-1/3}$. After that, we rigorously establish the uniqueness of this hierarchy. This allows us to conclude that the two-species Husimi measure from the solution of the $N$-particle Schrödinger equation approximates the solution of the Vlasov equation for two-species systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Derivation of Vlasov equations for multi-species fermions Chen, Hongshuo Chen, Li Lee, Jinyeop Sun, Zhiwei Mathematical Physics We explore a system of two-species fermions with $N$ particles. Through this exploration, we establish a two-species Husimi measure and construct a two-species Bogoliubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy with error terms. We provide proofs of the smallness of these errors in the semiclassical and mean-field limits, fixing $\hbar = N^{-1/3}$. After that, we rigorously establish the uniqueness of this hierarchy. This allows us to conclude that the two-species Husimi measure from the solution of the $N$-particle Schrödinger equation approximates the solution of the Vlasov equation for two-species systems. |
| title | Derivation of Vlasov equations for multi-species fermions |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2312.01075 |