Zeno product formula revisited
Pavel Exner, Takashi Ichinose, Hagen Neidhardt, and Valentin A., Zagrebnov
TL;DR
This paper introduces a new product formula involving projections and complex functions of operators, proving strong and operator-norm convergence under certain conditions, with applications to Zeno dynamics in quantum measurement theory.
Contribution
It presents a novel product formula combining projections and complex functions of operators, extending the mathematical framework for Zeno dynamics in quantum systems.
Findings
Proves strong convergence of the new product formula.
Establishes operator-norm convergence under restrictive assumptions.
Applies the formula to generalized quantum Zeno measurements.
Abstract
We introduce a new product formula which combines an orthogonal projection with a complex function of a non-negative operator. Under certain assumptions on the complex function the strong convergence of the product formula is shown. Under more restrictive assumptions even operator-norm convergence is verified. The mentioned formula can be used to describe Zeno dynamics in the situation when the usual non-decay measurement is replaced by a particular generalized observables in the sense of Davies.
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