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

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

2001-11-22

arxiv.org/abs/math-ph/0111042v3

Physics

Mathematical Physics

35 pages, latex

Scientific paper

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 Schr\"odinger equations.

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