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Derivation of the nonlinear Schrödinger equation from a many body Coulomb system

Laszlo Erdos·Horng-Tzer Yau
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Abstract

We consider the time evolution of N bosonic particles interacting via a mean field Coulomb potential. Suppose the initial state is a product wavefunction. We show that at any finite time the correlation functions factorize in the limit $N \to \infty$. Furthermore, the limiting one particle density matrix satisfies the nonlinear Hartree equation. The key ingredients are the uniqueness of the BBGKY hierarchy for the correlation functions and a new apriori estimate for the many-body Schrödinger equations.

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Laszlo Erdos, Horng-Tzer Yau. 2002-05-22. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. https://arxiv.org/abs/math-ph/0111042

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