Note on a Product Formula Related to Quantum Zeno Dynamics

Abstract

Given a nonnegative self-adjoint operator $H$ acting on a separable Hilbert space and an orthogonal projection $P$ such that $H_P:=(H^{1/2}P{)}^{\ast }(H^{1/2}P)$ is densely defined, we prove that ${\lim }_{n\to \infty }(P{\mathrm{e}}^{-itH/n}P{)}^n={\mathrm{e}}^{-it{H}_P}P$ 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 $P(0)=P$.

30 pages, no figures; to appear in Ann. H. Poincaré

References in corpus (1)

• Quantum Zeno dynamics: mathematical and physical aspects

Cited by in corpus (6)

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• Ultrastrong coupling, nonselective measurement and quantum Zeno dynamics
• Truncated quantum observables and their semiclassical limit
• The semiclassical limit of a quantum Zeno dynamics