A nonlinear Landau-Zener formula

Rémi Carles (1) , Clotilde Fermanian Kammerer (2)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées

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.

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Rémi Carles, Clotilde Fermanian Kammerer. A nonlinear Landau-Zener formula. Journal of Statistical Physics, 2013, 152 (4), pp.619-656. ⟨10.1007/s10955-013-0785-x⟩. ⟨hal-00759132v2⟩