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Asymptotic Analysis of the Fourier Transform of a Probability Measure with Application to Quantum Zeno Effect
| Title: | Asymptotic Analysis of the Fourier Transform of a Probability Measure with Application to Quantum Zeno Effect |
| Authors: | Arai, Asao Browse this author |
| Keywords: | quantum Zeno effect | | Hamiltonian | | probability measure | | asymptotic analysis |
| Issue Date: | 16-May-2012 |
| Publisher: | Department of Mathematics, Hokkaido University |
| Journal Title: | Hokkaido University Preprint Series in Mathematics |
| Volume: | 1008 |
| Start Page: | 1 |
| End Page: | 10 |
| Abstract: | Let μ be a R probability measure on the set R of real numbers and μˆ(t) := R e¡itλdμ(λ) (t 2 R) be the Fourier transform of μ (i is the imaginary unit). Then, under suitable conditions, asymptotic formulae of jˆμ(t/x)j2x in 1/x as x ! 1 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 ! 1. |
| Type: | bulletin (article) |
| URI: | http://hdl.handle.net/2115/69813 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > Hokkaido University Preprint Series in Mathematics
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Submitter: 数学紀要登録作業用
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