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arXiv · 1011.4773

Zeno effect and ergodicity in finite-time quantum measurements

D. Sokolovski
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Abstract

We demonstrate that an attempt to measure a non-local in time quantity, such as the time average $\la A\ra_T$ of a dynamical variable $A$, by separating Feynman paths into ever narrower exclusive classes traps the system in eigensubspaces of the corresponding operator $\a$. Conversely, in a long measurement of $\la A\ra_T$ to a finite accuracy, the system explores its Hilbert space and is driven to a universal steady state in which von Neumann ensemble average of $\a$ coincides with $\la A\ra_T$. Both effects are conveniently analysed in terms of singularities and critical points of the corresponding amplitude distribution and the Zeno-like behaviour is shown to be a consequence of conservation of probability.

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D. Sokolovski. 2011-05-10. Zeno effect and ergodicity in finite-time quantum measurements. https://doi.org/10.1103/physreva.84.062117

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