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 → ∞ and G → 0 while GN = λ fixed. In the super-critical regime of large λ, we introduce the regularized interaction where the cutoff vanishes as N → ∞. We show that the difference between the many-body semi-relativistic Schrödinger dynamics and the corresponding semi-relativistic Hartree dynamics is at most of order N −1 for all λ, i.e., the result covers the sub-critical regime and the super-critical regime. The N dependence of the bound is optimal.
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Communicated by Jan Derezinski.
Partially supported by Basic Science Research Program through the National Research Foundation of Korea Grant 2011-0013474.
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Lee, J.O. Rate of Convergence Towards Semi-Relativistic Hartree Dynamics. Ann. Henri Poincaré 14, 313–346 (2013). https://doi.org/10.1007/s00023-012-0188-6
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DOI: https://doi.org/10.1007/s00023-012-0188-6