Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

Details Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential Mean field propagation of infinite dimensional Wigner measures with a singular two-body interaction potential

2011-11-25

arxiv.org/abs/1111.5918v1

Mathematics

Analysis of PDEs

49 pages

Scientific paper

We consider the quantum dynamics of many bosons systems in the mean field limit with a singular pair-interaction potential, including the attractive or repulsive Coulombic case in three dimensions. By using a measure transportation technique, we show that Wigner measures propagate along the nonlinear Hartree flow. Such property was previously proved only for bounded potentials in our previous works with a slightly different strategy.

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