Zeno Dynamics of von Neumann Algebras
Andreas U. Schmidt
TL;DR
This paper explores the quantum Zeno effect within von Neumann algebras, revealing how Zeno dynamics can be characterized as modular dynamics on a localized subalgebra, linking modular operators through a Trotter product formula.
Contribution
It establishes a connection between Zeno dynamics and modular automorphisms in von Neumann algebras, providing a new mathematical framework for understanding the effect.
Findings
Zeno dynamics acts as automorphisms on a localized subalgebra
Under certain conditions, Zeno dynamics equals the modular dynamics of that subalgebra
The modular operators are related via a Kato-Lie-Trotter product formula
Abstract
The dynamical quantum Zeno effect is studied in the context of von Neumann algebras. We identify a localized subalgebra on which the Zeno dynamics acts by automorphisms. The Zeno dynamics coincides with the modular dynamics of that subalgebra, if an additional assumption is satisfied. This relates the modular operator of that subalgebra to the modular operator of the original algebra by a variant of the Kato-Lie-Trotter product formula.
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