108 research outputs found
Modelling by maps of two-frequency microwave ionization of hydrogen atoms
Mapping equations of motion of the highly exited classical atom in a
monochromatic field are generalized for the two-frequency microwave field.
Analysis of the obtained equations indicates to the weak sensitivity of the
position of the recently observed ionization peak near the main resonance to
the frequency and amplitude of the additional microwave field. In the high
frequency region, however, the sensitivity of the enhanced ionization peaks on
the additional field frequency is predicted.Comment: LaTex, 3 PostScript figure
Stochastic nonlinear differential equation generating 1/f noise
Starting from the simple point process model of 1/f noise we derive a
stochastic nonlinear differential equation for the signal exhibiting 1/f noise
in any desirably wide range of frequency. A stochastic differential equation
(the general Langevin equation with a multiplicative noise) that gives 1/f
noise is derived for the first time. The solution of the equation exhibits the
power-law distribution. The process with 1/f noise is demonstrated by the
numerical solution of the derived equation with the appropriate restriction of
the diffusion of the signal in some finite interval.Comment: 3 figure
Modelling financial markets by the multiplicative sequence of trades
We introduce the stochastic multiplicative point process modelling trading
activity of financial markets. Such a model system exhibits power-law spectral
density S(f) ~ 1/f**beta, scaled as power of frequency for various values of
beta between 0.5 and 2. Furthermore, we analyze the relation between the
power-law autocorrelations and the origin of the power-law probability
distribution of the trading activity. The model reproduces the spectral
properties of trading activity and explains the mechanism of power-law
distribution in real markets.Comment: 6 pages, 2 figure
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
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