12-57 Asao Arai
Asymptotic Analysis of the Fourier Transform of a Probability Measure with Application to Quantum Zeno Effect (131K, Latex 2e) May 15, 12
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Abstract. Let $\mu$ be a probability measure on the set $\BBR$ of real numbers and $\hat \mu(t):=\int_{\BBR}e^{-it\lambda}d\mu(\lambda)$ ($t\in \BBR$) be the Fourier transform of $\mu$ ($i$ is the imaginary unit). Then, under suitable conditions, asymptotic formulae of $|\hat \mu(t/x)|^{2x}$ in $1/x$ as $x o \infty$ are derived. These results are applied to the so-called quantum Zeno effect to establish asymptotic formulae of its occurrence probability in the inverse of the number $N$ of measurements made in a time interval as $N o\infty$.

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