Local exact controllability of a 1D Bose-Einstein condensate in a time-varying box

Karine Beauchard (1) , Horst Lange (2) , Teismann Holger (3)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 Mathematisches Institute
3 Department of Mathematics and Statistics

We consider a one dimensional Bose-Einstein condensate in a in finite square-well (box) potential. This is a nonlinear control system in which the state is the wave function of the Bose Einstein condensate and the control is the length of the box. We prove that local exact controllability around the ground state (associated with a fi xed length of the box) holds generically with respect to the chemical potential ; i.e. up to an at most countable set of values. The proof relies on the linearization principle and the inverse mapping theorem, as well as ideas from analytic perturbation theory.

Domaines: Equations aux dérivées partielles [math.AP]

Karine Beauchard, Horst Lange, Teismann Holger. Local exact controllability of a 1D Bose-Einstein condensate in a time-varying box. 2013. ⟨hal-00825796⟩