当前位置: X-MOL 学术Dyn. Partial Differ. Equ. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations
Dynamics of Partial Differential Equations ( IF 1.3 ) Pub Date : 2020-01-01 , DOI: 10.4310/dpde.2020.v17.n3.a4
A. Duca 1
Affiliation  

The aim of this work is to study the controllability of infinite bilinear Schr\"odinger equations on a segment. We consider the equations (BSE) $i\partial_t\psi^{j}=-\Delta\psi^j+u(t)B\psi^j$ in the Hilbert space $L^2((0,1),\mathbb{C})$ for every $j\in\mathbb{N}^*$. The Laplacian $-\Delta$ is equipped with Dirichlet homogeneous boundary conditions, $B$ is a bounded symmetric operator and $u\in L^2((0,T),\mathbb{R})$ with $T>0$. We prove the simultaneous local and global exact controllability of infinite (BSE) in projection. The local controllability is guaranteed for any positive time and we provide explicit examples of $B$ for which our theory is valid. In addition, we show that the controllability of infinite (BSE) in projection onto suitable finite dimensional spaces is equivalent to the controllability of a finite number of (BSE) (without projecting). In conclusion, we rephrase our controllability results in terms of density matrices.

中文翻译:

无限一维双线性薛定谔方程投影的同时全局精确可控性

我们证明了无限(BSE)在合适的有限维空间上投影的可控性等价于有限数量(BSE)(没有投影)的可控性。总之,我们根据密度矩阵重新表述我们的可控性结果。
更新日期:2020-01-01
down
wechat
bug