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arXiv · 2012.15061

Note on a Product Formula Related to Quantum Zeno Dynamics

Pavel Exner·Takashi Ichinose
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Abstract

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 $P(0)=P$.

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Pavel Exner, Takashi Ichinose. 2020-12-30. Note on a Product Formula Related to Quantum Zeno Dynamics. https://doi.org/10.1007/s00023-020-01014-z

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