Derivation of the two-dimensional nonlinear Schrodinger equation from many body quantum dynamics Citation
نویسندگان
چکیده
We derive rigorously, for both R and [−L,L], the cubic nonlinear Schrödinger 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.
منابع مشابه
DERIVATION OF THE TWO-DIMENSIONAL NONLINEAR SCHRÖDINGER EQUATION FROM MANY BODY QUANTUM DYNAMICS By KAY KIRKPATRICK, BENJAMIN SCHLEIN, and GIGLIOLA STAFFILANI
We derive rigorously, for both R2 and [−L, L]×2, the cubic nonlinear Schrödinger 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...
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