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Asymptotic expansion of the mean-field approximation. (arXiv:1710.03618v1 [quant-ph])
来源于:arXiv
We established and estimate the full asymptotic expansion in integer powers
of 1 N of the [ $\sqrt$ N ] first marginals of N-body evolutions lying in a
general paradigm containing Kac models and non-relativistic quantum evolution.
We prove that the coefficients of the expansion are, at any time, explicitly
computable given the knowledge of the linearization on the one-body meanfield
kinetic limit equation. Instead of working directly with the corresponding
BBGKY-type hierarchy, we follows a method developed in [22] for the meanfield
limit, dealing with error terms analogue to the v-functions used in previous
works. As a by-product we get that the rate of convergence to the meanfield
limit in 1 N is optimal. 查看全文>>