Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics
Mathematical Physics
2009-04-13 v2 Analysis of PDEs
math.MP
Abstract
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.
Keywords
Cite
@article{arxiv.0808.0505,
title = {Derivation of the two dimensional nonlinear Schrodinger equation from many body quantum dynamics},
author = {Kay Kirkpatrick and Benjamin Schlein and Gigliola Staffilani},
journal= {arXiv preprint arXiv:0808.0505},
year = {2009}
}
Comments
29 pages, 3 figures; reference added, typos fixed, section 7.2 simplified. To appear, American Journal of Mathematics