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arXiv · 1609.04754

Hartree Corrections in a Mean-field Limit for Fermions with Coulomb Interaction

Sören Petrat
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Abstract

We consider the many-body dynamics of fermions with Coulomb interaction in a mean-field scaling limit where the kinetic and potential energy are of the same order for large particle numbers. In the considered limit the spatial variation of the mean-field is small. We prove two results about this scaling limit. First, due to the small variation, i.e., small forces, we show that the many-body dynamics can be approximated by the free dynamics with an appropriate phase factor with the conjectured optimal error term. Second, we show that the Hartree dynamics gives a better approximation with a smaller error term. In this sense, assuming that the error term in the first result is optimal, we derive the Hartree equations from the many-body dynamics with Coulomb interaction in a mean-field scaling limit.

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Sören Petrat. 2017-05-24. Hartree Corrections in a Mean-field Limit for Fermions with Coulomb Interaction. https://doi.org/10.1088/1751-8121%2Faa6e0b

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