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Asymptotic analysis of the Fourier transform of a probability measure with application to the quantum Zeno effect
| Title: | Asymptotic analysis of the Fourier transform of a probability measure with application to the quantum Zeno effect |
| Authors: | Arai, Asao Browse this author →KAKEN DB |
| Keywords: | Quantum Zeno effect | | Hamiltonian | | Probability measure | | Asymptotic analysis |
| Issue Date: | 2013 |
| Journal Title: | Journal of Mathematical Analysis and Applications |
| Volume: | 403 |
| Issue: | 1 |
| Start Page: | 193 |
| End Page: | 199 |
| Publisher DOI: | 10.1016/j.jmaa.2013.02.020 |
| Abstract: | Let μμ be a probability measure on the set RR of real numbers and μˆ(t):=∫Re−itλdμ(λ) (t∈Rt∈R) be the Fourier transform of μμ (ii is the imaginary unit). Then, under suitable conditions, asymptotic formulae for |μˆ(t/x)|2x in 1/x1/x as x→∞x→∞ are derived. These results are applied to the so-called quantum Zeno effect to establish asymptotic formulae for its occurrence probability in the inverse of the number NN of measurements made in a time interval as N→∞N→∞. |
| Type: | article (author version) |
| URI: | http://hdl.handle.net/2115/52668 |
| Appears in Collections: | 理学院・理学研究院 (Graduate School of Science / Faculty of Science) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 新井 朝雄
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