 9964 Yu.E.KUZOVLEV
 Kinetical theory beyond conventional approximations and 1/fnoise
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Feb 28, 99

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Abstract. The theory of 1/fnoise is under consideration based on the idea
that 1/fnoise has no relation to longlasting 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 nonGaussianity of longrange statistics, both expressed
in terms of only shortrange characteristic scales.
The exact relations between 1/fnoise and equilibrium fourpoint
cumulants in thermodynamical systems are analysed. The presence of
longliving fourpoint 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 instate to outstate
inside the collision region. Due to this reason the BBGKY hierarchy as
considered under the BoltzmannGrad limit implies the infinite set of
kinetical equations which describe the evolution of manyparticle
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 selfdiffusion
in equilibrium gas. The peculiar behaviour of the fourorder cumulant of
Brownian displacement of a gas particle is found being identical to
1/ffluctuations of diffusivity and mobility. This is the example of
dynamical system which produces no slow processes but produces 1/fnoise.
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