Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics
| dc.creator | Kirkpatrick, Kay | |
| dc.creator | Schlein, Benjamin | |
| dc.creator | Staffilani, Gigliola | |
| dc.date | 2008-08-04 | |
| dc.date | 2009-04-13 | |
| dc.date.accessioned | 2026-07-07T13:02:16Z | |
| dc.date.available | 2026-07-07T13:02:16Z | |
| dc.description | 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. | |
| dc.description | 29 pages, 3 figures; reference added, typos fixed, section 7.2 simplified. To appear, American Journal of Mathematics | |
| dc.identifier | https://arxiv.org/abs/0808.0505 | |
| dc.identifier | http://arxiv.org/abs/0808.0505 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/226392 | |
| dc.subject | Mathematical Physics | |
| dc.subject | Analysis of PDEs | |
| dc.subject | 35Q55; 81V70; 11L07 | |
| dc.title | Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics | |
| dc.type | text |