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

L. Erdös, H. Yau, Advances in Theoretical and Mathematical Physics 5 (2001) 1169–1205.

Journal Article | Published
Author
Erdös, LászlóIST Austria ; Yau, Horng-Tzer
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 → ∞. 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
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.
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 5, no. 6 (2001): 1169–1205.
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, 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.
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