We prove that the Schrödinger equation is approximately controllable in Sobolev spaces , , 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 .
@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}, pages = {901--915}, publisher = {Elsevier}, volume = {27}, number = {3}, year = {2010}, doi = {10.1016/j.anihpc.2010.01.004}, mrnumber = {2629885}, zbl = {1191.35257}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.004/} }
TY - JOUR AU - Nersesyan, Vahagn TI - Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 901 EP - 915 VL - 27 IS - 3 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.004/ DO - 10.1016/j.anihpc.2010.01.004 LA - en ID - AIHPC_2010__27_3_901_0 ER -
%0 Journal Article %A Nersesyan, Vahagn %T Global approximate controllability for Schrödinger equation in higher Sobolev norms and applications %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 901-915 %V 27 %N 3 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.01.004/ %R 10.1016/j.anihpc.2010.01.004 %G en %F 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/articles/10.1016/j.anihpc.2010.01.004/
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