Product formula related to quantum Zeno dynamics

Abstract

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.

LaTeX 2e, 24 pages, with substantial modifications, to appear in Ann. H. Poincare

References in corpus (2)

• Zeno dynamics yields ordinary constraints
• Product formula related to quantum Zeno dynamics

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