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, LászlóISTA 
;
Yau, Horng
;
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
Publisher
International Press
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/0111042
Erdös, 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/0111042
Erdös, 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 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.
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.
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