Abstract
We present a new proof of the convergence of the N −particle Schrödinger 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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Communicated by H.-T. Yau.
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Fröhlich, J., Graffi, S. & Schwarz, S. Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons. Commun. Math. Phys. 271, 681–697 (2007). https://doi.org/10.1007/s00220-007-0207-5
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DOI: https://doi.org/10.1007/s00220-007-0207-5