06-87 J\"urg Fr\"ohlich, Sandro Graffi, Simon Schwarz

MEAN-FIELD- AND CLASSICAL LIMIT OF MANY-BODY SCHR\"ODINGER DYNAMICS FOR BOSONS (45K, Latex 2e) Mar 22, 06

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Abstract. We present a new proof of the convergence of the $N-$particle Schr\"odinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in $\hbar$, up to an exponentially small remainder. For $\hbar = 0$, the classical dynamics in the mean-field limit is given by the Vlasov equation.

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