Notions of controllability for quantum mechanical systems
Notions of controllability for quantum mechanical systems
复制标题
量子力学系统的可控性概念
DOI：
10.1109/cdc.2001.981126
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
D. D’Alessandro
中科院分区：
文献类型：
--
作者：
F. Albertini;D. D’Alessandro
在本文中，我们定义了三种不同的概念，涉及到的可能性驱动的演化算子以及系统的状态的量子力学系统的可控性。利用球面上变换群传递性的一般结果，我们建立了这些不同的可控性概念之间的联系。受多能级量子系统物理模型的启发，我们还研究了在紧变换李群上变化的系统在任意小时间内的能控性与相应的系统在相应的齐次空间上的能控性之间的关系。作为应用，我们证明了两个自旋为1/2的相互作用粒子系统的一个否定结果，即不是所有的态转移都能在任意时间内得到。
In this paper, we define three different notions of controllability for quantum mechanical systems involving the possibility of driving the evolution operator as well as the state of the system. By using general results on transitivity of transformation groups on spheres we establish the connections among these different notions of controllability. Motivated by the physical model of multilevel quantum systems, we also study the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove for the system of two interacting spin 1/2 particles the negative result that not every state transfer can be obtained in arbitrary time.