Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866914608771497984 |
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| author | Liang, Hao Wang, Zhenfu |
| author_facet | Liang, Hao Wang, Zhenfu |
| contents | We give a purification and fidelity formulation of the projection method for mixed Hartree data. For the mean-field evolution of $N$-particle density matrices, we prove quantitative propagation of chaos for all fixed marginals, first in squared Uhlmann fidelity and then in trace norm via the Fuchs--van de Graaf inequality. The argument applies a rank-one Pickl-type counting estimate in a purified one-particle space and uses monotonicity of fidelity under partial trace to return to the physical variables. The result allows singular interactions satisfying a projected-square bound, including $L^{2r}$ interactions and the Coulomb potential. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_28685 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics Liang, Hao Wang, Zhenfu Mathematical Physics 81V70 (Primary) 35Q55, 35Q40, 81P16 (Secondary) We give a purification and fidelity formulation of the projection method for mixed Hartree data. For the mean-field evolution of $N$-particle density matrices, we prove quantitative propagation of chaos for all fixed marginals, first in squared Uhlmann fidelity and then in trace norm via the Fuchs--van de Graaf inequality. The argument applies a rank-one Pickl-type counting estimate in a purified one-particle space and uses monotonicity of fidelity under partial trace to return to the physical variables. The result allows singular interactions satisfying a projected-square bound, including $L^{2r}$ interactions and the Coulomb potential. |
| title | Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics |
| topic | Mathematical Physics 81V70 (Primary) 35Q55, 35Q40, 81P16 (Secondary) |
| url | https://arxiv.org/abs/2605.28685 |