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arXiv · 0808.0505

Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics

Kay Kirkpatrick·Benjamin Schlein·Gigliola Staffilani
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Abstract

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. We first prove convergence of the solution of the BBGKY hierarchy, corresponding to the many-body systems, to a solution of the infinite Gross-Pitaevskii hierarchy, corresponding to the cubic NLS; and then we prove uniqueness for the infinite hierarchy, which requires number-theoretical techniques in the periodic case.

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Kay Kirkpatrick, Benjamin Schlein, Gigliola Staffilani. 2009-04-13. Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics. https://arxiv.org/abs/0808.0505

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