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- W3100653659 abstract "We consider the semi-relativistic system of $N$ gravitating Bosons with gravitation constant $G$. The time evolution of the system is described by the relativistic dispersion law, and we assume the mean-field scaling of the interaction where $N to infty$ and $G to 0$ while $GN = lambda$ fixed. In the super-critical regime of large $lambda$, we introduce the regularized interaction where the cutoff vanishes as $N to infty$. We show that the difference between the many-body semi-relativistic Schr{o}dinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order $N^{-1}$ for all $lambda$, i.e., the result covers the sub-critical regime and the super-critical regime. The $N$ dependence of the bound is optimal." @default.
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- W3100653659 date "2012-06-24" @default.
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- W3100653659 title "Rate of Convergence Towards Semi-Relativistic Hartree Dynamics" @default.
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- W3100653659 doi "https://doi.org/10.1007/s00023-012-0188-6" @default.
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