Minimal time for the bilinear control of Schrodinger equations

作者：Beauchard Karine^*; Coron Jean Michel; Teismann Holger

来源：Systems & Control Letters, 2014, 71: 1-6.

DOI：10.1016/j.sysconle.2014.06.009

• Schrodinger equation
• Quantum control
• Minimal time

We consider a quantum particle in a potential V(x) (x is an element of 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 L-2 (R-N, C)-sphere, in sufficiently large times T, as proved by Boscain, Caponigro, Chambrion and Sigalotti (2012). 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.

• 出版日期2014-9