论文标题
关于与量子zeno动力学有关的产品公式的注意
Note on a Product Formula Related to Quantum Zeno Dynamics
论文作者
论文摘要
给定一个非负式自动接合操作员$ h $作用于可分离的希尔伯特空间和正交投影$ p $，以至于$ h_p：=（h^{1/2} p）^*（h^{1/2} p）$密切定义，我们证明了那个$ \ \ righ_ \ right \ right \ infty} （p \，\ mathrm {e}^{ - ith/n} p）^n = \ mathrm {e}^{ - ith_p} p $保存在强操作员拓扑中。我们还会得出此产品公式的修改及其扩展到$ p $被满足$ p（0）= p $的强烈连续投影功能所取代时的情况。
Given a nonnegative self-adjoint operator $H$ acting on a separable Hilbert space and an orthogonal projection $P$ such that $H_P := (H^{1/2}P)^*(H^{1/2}P)$ is densely defined, we prove that $\lim_{n\rightarrow \infty} (P\,\mathrm{e}^{-itH/n}P)^n = \mathrm{e}^{-itH_P}P$ holds in the strong operator topology. We also derive modifications of this product formula and its extension to the situation when $P$ is replaced by a strongly continuous projection-valued function satisfying $P(0)=P$.
