Bilinear quantum systems on compact graphs: well-posedness and global exact controllability
Résumé
In the present work, we study the well-posedness and the controllability of the bilinear Schr\"odinger equation (BSE) on compact graphs. We study interpolation properties of the spaces $D(|-\Delta|^{s/2})$ for $s>0$, which lead to the well-posedness of the equation in $D(|-\Delta|^{s/2})$ with suitable $s\geq 3$. In such spaces, we attain the global exact controllability of the (BSE) and we provide examples of the main results involving star graphs and tadpole graphs.
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