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

Erdös L, Yau H. 2001. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Advances in Theoretical and Mathematical Physics. 5(6), 1169–1205.

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Author

Erdös, László

^{ISTA}^{}; Yau, HorngAbstract

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 → ∞. 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.

Publishing Year

Date Published

2001-11-01

Journal Title

Advances in Theoretical and Mathematical Physics

Volume

5

Issue

6

Page

1169 - 1205

ISSN

IST-REx-ID

### Cite this

Erdös L, Yau H. Derivation of the nonlinear Schrödinger equation from a many body Coulomb system.

*Advances in Theoretical and Mathematical Physics*. 2001;5(6):1169-1205. doi:10.48550/arXiv.math-ph/0111042Erdös, L., & Yau, H. (2001). Derivation of the nonlinear Schrödinger equation from a many body Coulomb system.

*Advances in Theoretical and Mathematical Physics*. International Press. https://doi.org/10.48550/arXiv.math-ph/0111042Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.”

*Advances in Theoretical and Mathematical Physics*. International Press, 2001. https://doi.org/10.48550/arXiv.math-ph/0111042.L. Erdös and H. Yau, “Derivation of the nonlinear Schrödinger equation from a many body Coulomb system,”

*Advances in Theoretical and Mathematical Physics*, vol. 5, no. 6. International Press, pp. 1169–1205, 2001.Erdös, László, and Horng Yau. “Derivation of the Nonlinear Schrödinger Equation from a Many Body Coulomb System.”

*Advances in Theoretical and Mathematical Physics*, vol. 5, no. 6, International Press, 2001, pp. 1169–205, doi:10.48550/arXiv.math-ph/0111042.**All files available under the following license(s):**

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arXiv math-ph/0111042