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Mean-Field- and Classical Limit of Many-Body Schrödinger Dynamics for Bosons

2007; Springer Science+Business Media; Volume: 271; Issue: 3 Linguagem: Inglês

10.1007/s00220-007-0207-5

1432-0916

Jürg Fröhlich, Sandro Graffi, Simon Schwarz,

Quantum Mechanics and Applications

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.