BBGKY equations, self-diffusion and 1/f noise in a slightly nonideal gas

Abstract

The hypothesis of ``molecular chaos'' is shown to fail when applied to spatially inhomogeneous evolution of a low-density gas, because this hypothesis is incompatible with reduction of interactions of gas particles to ``collisions''. The failure of molecular chaos means existence of statistical correlations between colliding and closely spaced particles in configuration space. If this fact is taken into account, then in the collisional approximation (in the kinetic stage of gas evolution) in the limit of infinitely small gas parameter the Bogolyubov-Born-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations yields an autonomous system of kinetic equations for the many-particle distribution functions of closely spaced particles. This system of equations can produce the Boltzmann equation only in the homogeneous case. It is used to analyze statistical properties of Brownian motion of a test gas particle. The analysis shows that there exist fluctuations with a 1/f spectrum in the diffusivity and mobility of any particle. The physical cause of these fluctuations is randomness of distribution of particles' encounters over the impact parameter values and, consequently, randomness of the rate and efficiency of collisions. In essence, this is {\bf reprint} of the like author's paper published in Russian in [ Zh. Eksp. Teor. Fiz. {\bf 94} (12), 140-156 (Dec. 1988)] and translated into English in [ Sov. Phys. JETP {\bf 67} (12), 469-2477 (Dec. 1988)] twenty years ago but seemingly still unknown to those to whom it might be very useful. The footnotes contain presently added comments.