DERIVATION OF THE TWO-DIMENSIONAL NONLINEAR SCHRODINGER EQUATION FROM MANY BODY QUANTUM DYNAMICS

作者：Kirkpatrick Kay^*; Schlein Benjamin; Staffilani Gigliola

来源：American Journal of Mathematics, 2011, 133(1): 91-130.

We derive rigorously, for both R(2) and [-L, L](x2), 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.

• 出版日期2011-2