A product formula related to quantum zeno dynamics
A product formula related to quantum zeno dynamics
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DOI：
10.1007/s00023-005-0203-2
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发表时间：
2005-04-01
影响因子：
1.5
通讯作者：
Ichinose, T
中科院分区：
文献类型：
--
作者：
Exner, P;Ichinose, T
我们证明了一个乘积公式，该公式涉及由半有界自伴算子生成的酉群和可分离希尔伯特空间 H 上的正交投影 P，并且收敛于 L-loc(2)(R; H)。它给出了关于子空间 Ran P 中描述量子芝诺动力学的极限是否存在的问题的部分答案。H 的收敛性在有限维 P 的情况下得到证明。主要结果在示例中说明，其中投影对应于 R-d 中的域，酉群是自由薛定谔演化。
We prove a product formula which involves the unitary group generated by a semibounded self-adjoint operator and an orthogonal projection P on a separable Hilbert space H, with the convergence in L-loc(2)(R; H). It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace Ran P. The convergence in H is demonstrated in the case of a finite-dimensional P. The main result is illustrated in the example where the projection corresponds to a domain in R-d and the unitary group is the free Schrodinger evolution.