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arXiv · 1708.07278

Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential

Li Chen·Ji Oon Lee·Jinyeop Lee
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Abstract

We consider a system of $N$-Bosons with a two-body interaction potential $V \in L^2(\mathbb{R}^3)+L^\infty(\mathbb{R}^3)$, possibly singular than the Coulomb interaction. We show that, with $H^1(\mathbb{R}^3)$ initial data, the difference between the many-body Schr\"odinger evolution in the mean-field regime and the corresponding Hartree dynamics is of order $1/N$, for any fixed time. The $N$-dependence of the bound is optimal.

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Li Chen, Ji Oon Lee, Jinyeop Lee. 2017-08-24. Rate of Convergence towards Hartree Dynamics with Singular Interaction Potential. https://doi.org/10.1063/1.5003665

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