A nonlinear Landau-Zener formula
Analysis of PDEs
2013-08-20 v2 Mathematical Physics
math.MP
Abstract
We consider a system of two coupled ordinary differential equations which appears as an envelope equation in Bose-Einstein Condensation. This system can be viewed as a nonlinear extension of the celebrated model introduced by Landau and Zener. We show how the nonlinear system may appear from different physical models. We focus our attention on the large time behavior of the solution. We show the existence of a nonlinear scattering operator, which is reminiscent of long range scattering for the nonlinear Schrodinger equation, and which can be compared with its linear counterpart.
Cite
@article{arxiv.1211.7195,
title = {A nonlinear Landau-Zener formula},
author = {Rémi Carles and Clotilde Fermanian Kammerer},
journal= {arXiv preprint arXiv:1211.7195},
year = {2013}
}
Comments
33 pages. Major revision in order to fix a flaw in the case F_1 != F_2 (the case F_1=F_2 is substantially simplified)