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We derive rigorously, for both R^2 and [-L, L]^2, the cubic nonlinear Schrodinger equation in a suitable scaling limit from the two-dimensional many-body Bose systems with short-scale repulsive pair interactions.
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L. Erdős and H.-T. Yau, Derivation of the nonlinear Schrödinger equation from a many body Coulomb system. Adv. Theor. Math. Phys
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J. Bourgain, On Strichartz inequalities and the nonlinear Schrodinger equation on irrational tori, preprint
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L. Erdős, B. Schlein, and H.-T. Yau, Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate. Preprint arXiv:math-ph/0606017. To appear in Ann. Math
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I. Rodnianski and B. Schlein, Quantum fluctuations and rate of convergence towards mean field dynamics. Preprint arXiv:math-ph/0711.3087
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L. Erdős, B. Schlein, and H.-T. Yau, Derivation of the cubic non-linear Schrödinger equation from quantum dynamics of many-body systems. Invent. Math
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S. Klainerman and M. Machedon, On the uniqueness of solutions to the Gross-Pitaevskii hierarchy. Comm. Math. Phys
2008
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