Derivation of the two-dimensional nonlinear Schrodinger equation from many body quantum dynamics
We derive rigorously, for both ${\Bbb R}^2$ and $[{-}L,L]^{\times 2}$, the cubic nonlinear Schr\"odinger 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 hie...
| Main Authors: | , , |
|---|---|
| Other Authors: | |
| Format: | Article |
| Language: | English |
| Published: |
Johns Hopkins University Press,
2012-07-26T13:11:35Z.
|
| Subjects: | |
| Online Access: | Get fulltext |
| Summary: | We derive rigorously, for both ${\Bbb R}^2$ and $[{-}L,L]^{\times 2}$, the cubic nonlinear Schr\"odinger 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. National Science Foundation (U.S.) (postdoctoral research fellowship DMS-0703618) National Science Foundation (U.S.) (grant DMS-0602678) |
|---|