Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, p. 901-915
We prove that the Schrödinger equation is approximately controllable in Sobolev spaces ${H}^{s}$, $s>0$, generically with respect to the potential. We give two applications of this result. First, in the case of one space dimension, combining our result with a local exact controllability property, we get the global exact controllability of the system in higher Sobolev spaces. Then we prove that the Schrödinger equation with a potential which has a random time-dependent amplitude admits at most one stationary measure on the unit sphere S in ${L}^{2}$.
@article{AIHPC_2010__27_3_901_0,
author = {Nersesyan, Vahagn},
title = {Global approximate controllability for Schr\"odinger equation in higher Sobolev norms and applications},
journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
publisher = {Elsevier},
volume = {27},
number = {3},
year = {2010},
pages = {901-915},
doi = {10.1016/j.anihpc.2010.01.004},
zbl = {1191.35257},
mrnumber = {2629885},
language = {en},
url = {http://www.numdam.org/item/AIHPC_2010__27_3_901_0}
}

Nersesyan, Vahagn. Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 3, pp. 901-915. doi : 10.1016/j.anihpc.2010.01.004. http://www.numdam.org/item/AIHPC_2010__27_3_901_0/

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