Related papers: Note on a Product Formula Related to Quantum Zeno Dynamics

Note on a Product Formula Related to Quantum Zeno Dynamics

URL: http://arxiv.org/abs/2012.15061v1
Date: Wed, 30 Dec 2020 07:04:41 GMT
Title: Note on a Product Formula Related to Quantum Zeno Dynamics
Authors: Pavel Exner and Takashi Ichinose
Abstract summary: We prove that $lim_nrightarrow infty (P,mathrme-itH/nP)n = mathrme-itH_PP$ holds in the strong operator topology. We derive modifications of this product formula and its extension to the situation when $P$ is replaced by a strongly continuous projection-valued function satisfying $P(0)=P$.
Score: 0.0
License: http://creativecommons.org/licenses/by/4.0/
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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