2023-04-02T02:56:19Zhttps://eprints.lib.hokudai.ac.jp/dspace-oai/requestoai:eprints.lib.hokudai.ac.jp:2115/698132022-11-17T02:08:08Zhdl_2115_45007hdl_2115_116Asymptotic Analysis of the Fourier Transform of a Probability Measure with Application to Quantum Zeno EffectArai, Asaoquantum Zeno effectHamiltonianprobability measureasymptotic analysis410Let 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.Department of Mathematics, Hokkaido UniversityDepartmental Bulletin Paperapplication/pdfhttp://hdl.handle.net/2115/69813info:doi/10.14943/84154https://eprints.lib.hokudai.ac.jp/dspace/bitstream/2115/69813/1/pre1008.pdfHokkaido University Preprint Series in Mathematics10081102012-05-16engpublisher