科研之友
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摘要
In the framework of bilinear control of the Schrodinger equation, it has been proved that the reachable set has a dense complement in S boolean AND H(2). Hence, in this setting, exact quantum control in infinite dimensions is not possible. On the other hand, it is known that there is a simple choice of operators which, when applied to an arbitrary state, generate dense orbits in Hilbert space. Compatibility of these two results is established in this paper and, in particular, it is proved that the closure of the reachable set of bilinear control is dense in S boolean AND H(2). The requirements for controllability in infinite dimensions are also related to the properties of the infinite-dimensional unitary group.
- 出版日期2011-4-1
