Asymptotic analysis of the Fourier transform of a probability measure with application to the quantum Zeno effect

作者：Arai Asao^*

来源：Journal of Mathematical Analysis and Applications, 2013, 403(1): 193-199.

DOI：10.1016/j.jmaa.2013.02.020

• Quantum Zeno effect
• Hamiltonian
• Probability measure
• Asymptotic analysis

Let mu be a probability measure on the set R of real numbers and (mu) over cap (t) := integral(R) e(-it lambda)d mu(lambda) (t is an element of R) be the Fourier transform of mu (i is the imaginary unit). Then, under suitable conditions, asymptotic formulae for vertical bar(mu) over cap (t/x)vertical bar(2x) in 1/x as x -%26gt; infinity 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 N of measurements made in a time interval as N -%26gt; infinity.

• 出版日期2013-7-1