526 research outputs found
Continuous transition from the extensive to the non-extensive statistics in an agent-based herding model
Systems with long-range interactions often exhibit power-law distributions
and can by described by the non-extensive statistical mechanics framework
proposed by Tsallis. In this contribution we consider a simple model
reproducing continuous transition from the extensive to the non-extensive
statistics. The considered model is composed of agents interacting among
themselves on a certain network topology. To generate the underlying network we
propose a new network formation algorithm, in which the mean degree scales
sub-linearly with a number of nodes in the network (the scaling depends on a
single parameter). By changing this parameter we are able to continuously
transition from short-range to long-range interactions in the agent-based
model.Comment: 12 pages, 6 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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