Large-time limit of the quantum Zeno effect

Paolo Facchi; Marilena Ligabò

doi:10.1063/1.4978851

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arXiv · 1702.04284

Large-time limit of the quantum Zeno effect

Paolo Facchi·Marilena Ligabò

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Abstract

If very frequent periodic measurements ascertain whether a quantum system is still in its initial state, its evolution is hindered. This peculiar phenomenon is called quantum Zeno effect. We investigate the large-time limit of the survival probability as the total observation time scales as a power of the measurement frequency, $t\propto N^\alpha$. The limit survival probability exhibits a sudden jump from 1 to 0 at $\alpha=1/2$, the threshold between the quantum Zeno effect and a diffusive behavior. Moreover, we show that for $\alpha\geq 1$ the limit probability becomes sensitive to the spectral properties of the initial state and to arithmetic properties of the measurement periods.

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Paolo Facchi, Marilena Ligabò. 2017-02-14. Large-time limit of the quantum Zeno effect. https://doi.org/10.1063/1.4978851

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