Yu.E.KUZOVLEV
Kinetical theory beyond conventional approximations and 1/f-noise
(123K, LaTex)
ABSTRACT. The theory of 1/f-noise is under consideration based on the idea
that 1/f-noise has no relation to long-lasting processes but originates
from the same dynamical mechanisms what are responsible for the loss of
causal correlations with the past, shot noise and fast relaxation.
The phenomenological theory of memoryless random flows of events and
of related Brownian motion is presented which closely connects 1/f
spectrum and non-Gaussianity of long-range statistics, both expressed
in terms of only short-range characteristic scales.
The exact relations between 1/f-noise and equilibrium four-point
cumulants in thermodynamical systems are analysed. The presence of
long-living four-point correlations and flicker noise in the Kac's
ring model is demonstrated.
The general idea is confirmed in the case of gas. It is shown that
the correct construction of gas kinetics in terms of Boltzmannian
collision operators needs in the ansatz whose meaning is conservation
of particles and probabilities at the path from in-state to out-state
inside the collision region. Due to this reason the BBGKY hierarchy as
considered under the Boltzmann-Grad limit implies the infinite set of
kinetical equations which describe the evolution of many-particle
probability distributions on the hypersurfaces corresponding to
encounters and collisions of particles. These equations reduce to usual
Boltzmann equation only in the spatially uniform case, but in general
forbid the molecular chaos.
The formulated kinetics are applied to statistics of self-diffusion
in equilibrium gas. The peculiar behaviour of the four-order cumulant of
Brownian displacement of a gas particle is found being identical to
1/f-fluctuations of diffusivity and mobility. This is the example of
dynamical system which produces no slow processes but produces 1/f-noise.