Time problem in quantum mechanics and its analysis by the concept of weak measurement

The model of weak measurements is applied to various problems, related to the time problem in quantum mechanics. The review and generalization of the theoretical analysis of the time problem in quantum mechanics based on the concept of weak measurements are presented. A question of the time interval the system spends in the specified state, when the final state of the system is given, is raised. Using the concept of weak measurements the expression for such time is obtained. The results are applied to the tunneling problem. A procedure for the calculation of the asymptotic tunneling and reflection times is proposed. Examples for delta-form and rectangular barrier illustrate the obtained results. Using the concept of weak measurements the arrival time probability distribution is defined by analogy with the classical mechanics. The proposed procedure is suitable to the free particles and to particles subjected to an external potential, as well. It is shown that such an approach imposes an inherent limitation to the accuracy of the arrival time definition.Comment: 13 figure

1/f noise from nonlinear stochastic differential equations

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f^b noise, and provides further insights into the origin of 1/f^b noise

Point Process Models of 1/f Noise and Internet Traffic

We present a simple model reproducing the long-range autocorrelations and the power spectrum of the web traffic. The model assumes the traffic as Poisson flow of files with size distributed according to the power-law. In this model the long-range autocorrelations are independent of the network properties as well as of inter-packet time distribution.Comment: 6 pages, 2 figures, CNET2004 Proceedings AI