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

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

2008-08-04

arxiv.org/abs/0808.0505v2

Physics

Mathematical Physics

29 pages, 3 figures; reference added, typos fixed, section 7.2 simplified. To appear, American Journal of Mathematics

Scientific paper

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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