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

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

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Title: Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems
Author: Erdos, Laszlo; Schlein, Benjamin; Yau, Horng-Tzer

Note: Order does not necessarily reflect citation order of authors.

Citation: Erdos, László, Benjamin Schlein, and Horng-Tzer Yau. 2006. “Derivation of the Cubic Non-Linear Schrödinger Equation from Quantum Dynamics of Many-Body Systems.” Inventiones Mathematicae 167 (3) (December 20): 515–614. doi:10.1007/s00222-006-0022-1.
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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.
Published Version: doi:10.1007/s00222-006-0022-1
Other Sources: https://arxiv.org/abs/math-ph/0508010
Terms of Use: This article is made available under the terms and conditions applicable to Other Posted Material, as set forth at http://nrs.harvard.edu/urn-3:HUL.InstRepos:dash.current.terms-of-use#LAA
Citable link to this page: http://nrs.harvard.edu/urn-3:HUL.InstRepos:32706730
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