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- W3097314744 abstract "The aim of this work is to study the controllability of the bilinear Schrödinger equation on compact graphs. In particular, we consider the equation $(BSE)$ $ipartial_tpsi=-Deltapsi+u(t)Bpsi$ in the Hilbert space $L^2(mathscr{G},mathbb{C})$, with $mathscr{G}$ being a compact graph. The Laplacian $-Delta$ is equipped with self-adjoint boundary conditions, $B$ is a bounded symmetric operator, and $uin L^2((0,T),mathbb{R})$ with $T>0$. We provide a new technique leading to the global exact controllability of $(BSE)$ in $D(|Delta|^{s/2})$ with $sgeq 3$. Afterwards, we introduce the “energetic controllability,” a weaker notion of controllability useful when the global exact controllability fails. In conclusion, we develop some applications of the main results involving, for instance, star graphs." @default.
- W3097314744 created "2020-11-09" @default.
- W3097314744 creator A5066750573 @default.
- W3097314744 date "2020-01-01" @default.
- W3097314744 modified "2023-10-17" @default.
- W3097314744 title "Global Exact Controllability of Bilinear Quantum Systems on Compact Graphs and Energetic Controllability" @default.
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- W3097314744 doi "https://doi.org/10.1137/18m1212768" @default.
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