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arXiv · 2605.28685

Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics

Hao Liang·Zhenfu Wang
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Abstract

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.

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Hao Liang, Zhenfu Wang. 2026-05-27. Purified Projection Method and Uhlmann Fidelity for Mixed Hartree Dynamics. https://arxiv.org/abs/2605.28685

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