Minimal time for the bilinear control of Schr\"odinger equations
Analysis of PDEs
2014-01-28 v1
Abstract
We consider a quantum particle in a potential V (x) (x in R^N) subject to a (spatially homogeneous) time-dependent electric field E(t), which plays the role of the control. Under generic assumptions on V, this system is approximately controllable on the L2(R^N;C)-sphere, in su ffiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti. In the present article, we show that this approximate controllability result is false in small time. As a consequence, the result by Boscain et al. is, in some sense, optimal with respect to the control time T.
Keywords
Cite
@article{arxiv.1401.6828,
title = {Minimal time for the bilinear control of Schr\"odinger equations},
author = {Karine Beauchard and Jean-Michel Coron and Holger Teismann},
journal= {arXiv preprint arXiv:1401.6828},
year = {2014}
}