Kinetical theory beyond conventional approximations and 1/f-noise (123K, LaTex) Feb 28, 99
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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.

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