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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2205.04513 |
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| _version_ | 1866913334575497216 |
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| author | Chen, Li Lee, Jinyeop Li, Yue Liew, Matthew |
| author_facet | Chen, Li Lee, Jinyeop Li, Yue Liew, Matthew |
| contents | We re-examine the combined semi-classical and mean-field limit in the $N$-body fermionic Schrödinger equation with pure state initial data using the Husimi measure framework. The Husimi measure equation involves three residue types: kinetic, semiclassical, and mean-field. The main result of this paper is to provide better estimates for the kinetic and mean-field residue than those in \cite{Chen2021JSP}. Especially, the estimate for the mean-field residue is shown to be smaller than the semiclassical residue by a mixed-norm estimate of the two-particle reduced density matrix factorization. Our analysis also updates the oscillation estimate parts in the residual term estimates appeared in \cite{Chen2021JSP}. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04513 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation Chen, Li Lee, Jinyeop Li, Yue Liew, Matthew Mathematical Physics We re-examine the combined semi-classical and mean-field limit in the $N$-body fermionic Schrödinger equation with pure state initial data using the Husimi measure framework. The Husimi measure equation involves three residue types: kinetic, semiclassical, and mean-field. The main result of this paper is to provide better estimates for the kinetic and mean-field residue than those in \cite{Chen2021JSP}. Especially, the estimate for the mean-field residue is shown to be smaller than the semiclassical residue by a mixed-norm estimate of the two-particle reduced density matrix factorization. Our analysis also updates the oscillation estimate parts in the residual term estimates appeared in \cite{Chen2021JSP}. |
| title | A mixed-norm estimate of the two-particle reduced density matrix of many-body Schrödinger dynamics for deriving the Vlasov equation |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2205.04513 |