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arXiv math-ph/0302060math-phmath.MPquant-ph
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与量子芝诺动力学有关的乘积公式

Product formula related to quantum Zeno dynamics

P. Exner, T. Ichinose

备注：
LaTeX 2e, 24 pages, with substantial modifications, to appear in Ann. H. Poincare
发表信息：
Ann. H. Poincare 6 (2005), 195-215
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摘要：

证明了可分Hilbert空间$\HH$上半有界自伴算子与正交投影$P$生成的酉群的乘积公式，并证明了该乘积公式收敛于$L^2_\mathrm{loc}(\mathbb{R};\HH)$ .部分回答了描述量子Zeno动力学的极限在子空间\hbox{$\mathrm{Ran} P$}中的存在性问题。在有限维$P$的情况下证明了$\HH$的收敛性。主要结果在投影对应于$\mathbb{R}^d$中的一个域并且酉群是自由薛定谔演化的例子中得到说明。

英文摘要：

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 $\HH$, with the convergence in $L^2_\mathrm{loc}(\mathbb{R};\HH)$. It gives a partial answer to the question about existence of the limit which describes quantum Zeno dynamics in the subspace \hbox{$\mathrm{Ran} P$}. The convergence in $\HH$ 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 $\mathbb{R}^d$ and the unitary group is the free Schrödinger evolution.

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