Note on a Product Formula Related to Quantum Zeno Dynamics

DOI10.1007/S00023-020-01014-ZarXiv2012.15061MaRDI QIDQ6357201

Pavel Exner, Takashi Ichinose

Publication date: 30 December 2020

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 $li{m}_{nightarrowinfty}(P,mathrm{e}^{-itH/n}P{)}^n=mathrm{e}^{-it{H}_P}P$ 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 $P(0)=P$.

Mathematics Subject Classification ID

Special classes of linear operators (47Bxx) Groups and semigroups of linear operators, their generalizations and applications (47Dxx) Nonlinear operators and their properties (47Hxx)

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