Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems

L. Erdös, B. Schlein, H. Yau, Inventiones Mathematicae 167 (2007) 515–614.

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Abstract
We prove rigorously that the one-particle density matrix of three dimensional interacting Bose systems with a short-scale repulsive pair interaction converges to the solution of the cubic non-linear Schrödinger equation in a suitable scaling limit. The result is extended to k-particle density matrices for all positive integer k.
Publishing Year
Date Published
2007-03-01
Journal Title
Inventiones Mathematicae
Volume
167
Issue
3
Page
515 - 614
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Erdös L, Schlein B, Yau H. Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. 2007;167(3):515-614. doi:10.1007/s00222-006-0022-1
Erdös, L., Schlein, B., & Yau, H. (2007). Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. Springer. https://doi.org/10.1007/s00222-006-0022-1
Erdös, László, Benjamin Schlein, and Horng Yau. “Derivation of the Cubic Non Linear Schrödinger Equation from Quantum Dynamics of Many Body Systems.” Inventiones Mathematicae. Springer, 2007. https://doi.org/10.1007/s00222-006-0022-1.
L. Erdös, B. Schlein, and H. Yau, “Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems,” Inventiones Mathematicae, vol. 167, no. 3. Springer, pp. 515–614, 2007.
Erdös L, Schlein B, Yau H. 2007. Derivation of the cubic non linear Schrödinger equation from quantum dynamics of many body systems. Inventiones Mathematicae. 167(3), 515–614.
Erdös, László, et al. “Derivation of the Cubic Non Linear Schrödinger Equation from Quantum Dynamics of Many Body Systems.” Inventiones Mathematicae, vol. 167, no. 3, Springer, 2007, pp. 515–614, doi:10.1007/s00222-006-0022-1.

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