Mean-Field Approximation of Quantum Systems and Classical Limit

2002/05/22 by Sandro Graffi, Graffi, Sandro, Andre' Martinez +3 · 2 citations
Mathematics · Physics and Astronomy · #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP

paper · pdf · doi:10.48550/arxiv.math-ph/0205033

arxiv created 2002/05/22 · arxiv updated 2009/11/30

Abstract

We prove that, for a smooth two-body potentials, the quantum mean-field approximation to the nonlinear Schroedinger equation of the Hartree type is stable at the classical limit h → 0, yielding the classical Vlasov equation.

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• An Egorov Theorem for Wasserstein Distances
• Semi-classical limit of quantum scattering states for the nonlinear Hartree equation

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